Uplink precoding method in 4-Tx system

ABSTRACT

A method for a user equipment to precode and transmit an uplink signal efficiently in a 4-antenna system and a method for a base station to receive the transmitted signal efficiently are disclosed. Four antennas of a user equipment can be grouped by a 2-antenna unit. In consideration of this antenna group, it is able to perform precoding using antenna selection/DFT matrix of the antenna group unit. Moreover, a rank-3 codebook can be configured to include a precoding matrix of a type in consideration of power balance per antenna and a precoding matrix including one non-zero component only in one row for maintaining a good CM property.

CROSS REFERENCE TO RELATED APPLICATIONS

Pursuant to 35 U.S.C. 119, this application claims the benefit ofearlier filing date and right of priority to Korean Patent ApplicationNo. 10-2009-0127920, filed on Dec. 21, 2009, and also claims the benefitof U.S. Provisional Application Nos. 61/152,476, 61/153,943, 61/156,544,61/163,056, 61/171,071, 61/176,094 and 61/218,437, filed on Feb. 13,2009, Feb. 19, 2009, Mar. 2, 2009, Mar. 25, 2009, Apr. 20, 2009, May 6,2009 and Jun. 19, 2009, respectively, the contents of which are allhereby incorporated by reference herein in their entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a technology for transmitting/receivingsignals through precoding in a mobile communication system, and moreparticularly, to a method for a user equipment to precode and transmitan uplink signal efficiently in a 4-antenna system and a method for abase station to receive the transmitted signal efficiently.

2. Discussion of the Related Art

In a multi-antenna or MIMO system, precoding provides high peak/averagesystem throughput by providing a beamforming gain and a diversity gainto a transmitting/receiving side. Yet, a precoding scheme needs to beappropriately designed in consideration of antenna setting, channelconfiguration, system structure and the like.

Generally, an MIMO system performs precoding to minimize complexity andcontrol signaling overhead using a codebook based precoding scheme. Inthis case, a codebook includes a scribed number of precodingvectors/matrixes predetermined between transmitting and receiving sidesaccording to a transmission rank and the number of antennas. Thetransmitting side selects a specific vector/matrix within the codebookaccording to channel status information received from the receivingside, perform precoding on a transmission signal, and then transmits theprecoded signal. Occasionally, the transmitting side selects a precodingmatrix according to a predetermined rule instead of receiving thechannel status information from the receiving side, performs precodingand is then able to transmit a corresponding signal.

FIG. 1 is a diagram for explaining a basic concept of codebook basedprecoding.

According to a codebook based precoding scheme, as mentioned in theforegoing description, a transmitting side and a receiving side sharecodebook information including a prescribed number of precoding matrixespredetermined according to a transmission rank, the number of antennasand the like with each other. The receiving side measures a channelstatus via a received signal and is then able to feed back preferredprecoding matrix information to the transmitting side based on theaforesaid codebook information. FIG. 1 shows that the receiving sidetransmits preferred precoding matrix information per codeword to thetransmitting side, for example.

Having received the feedback information from the receiving side, thetransmitting side is able to select a specific precoding matrix from thecodebook based on the received information. Having selected theprecoding matrix, the transmitting side performs precoding in a mannerof multiplying layer signals, of which number corresponds to atransmission rank, by the selected precoding matrix. And, thetransmitting side is able to transmit the precoded transmission signalvia a plurality of antennas. Having received the signal precoded andtransmitted by the transmitting side, the receiving side is able toreconstruct the received signal by performing a process reverse to theprecoding performed by the transmitting side. As a precoding matrixgenerally meets such a condition of a unitary matrix (U) as U*U^(H)=I,the reverse processing of the above precoding can be performed in amanner of multiplying a received signal by Hermitian (P^(H)) of aprecoding matrix (P) used for the precoding of the transmitting side.

In LTE (3^(RD) Generation Partnership Project Long Term Evolution)release 8 system, in case of applying MIMO scheme to an uplink signaltransmission to a base station from a user equipment, an MIMOtransmission scheme is prescribed for a downlink signal transmissionfrom a base station to a user equipment only due to such a problem asPAPR/CM (peak-to-average ratio/cubic metric) property degradation andthe like. Yet, an uplink signal transmitted by a user equipment to abase station is ongoing to be discussed in a direction of applying MIMOscheme for transmission rate increase, diversity gain acquisition andthe like. And, a next standard of 3GPP LTE system is ongoing to discussabout a detailed method of applying MIMO scheme to an uplink signaltransmission.

SUMMARY OF THE INVENTION

Accordingly, the present invention is directed to an uplink precodingmethod in 4 Tx system that substantially obviates one or more problemsdue to limitations and disadvantages of the related art.

An object of the present invention is to provide a codebook for uplinkprecoding, and more particularly, a codebook suitable for a userequipment to precode and transmit a signal efficiently using 4 antennas.

Another object of the present invention is to provide a method oftransmitting a signal to a base station from a user equipment using 4antennas.

The technical objects realized and attained by the present invention arenon-limited to the above mentioned objects. And, other unmentionedtechnical tasks can be taken into consideration by those having ordinaryskill in the art, to which the present invention pertains, uponexamination of the following embodiments of the present invention.

To achieve these objects and other advantages and in accordance with thepurpose of the invention, as embodied and broadly described herein, amethod of transmitting a signal, which is transmitted to a base stationby a user equipment configured to use 4 antennas, according to thepresent invention includes the steps of obtaining transmission rankinformation, outputting a precoded signal by selecting one precodingmatrix corresponding to the transmission rank from a 4-antenna codebookand then performing precoding on layer signals of which numbercorresponds to the transmission rank, and transmitting the precodedsignal to the base station, wherein the 4 antennas are grouped into afirst antenna group including two of the 4 antennas and a second antennagroup including the rest of the 4 antennas and wherein the 4-antennacodebook includes a first type precoding matrix, in which two componentscorresponding to the first antenna group are zero and two componentscorresponding to the second antenna group construct a DFT matrix, and asecond type precoding matrix, in which two components corresponding tothe first antenna group and two components corresponding to the secondantenna group construct DFT matrixes, respectively, for a rank 1.

Preferably, the first type precoding matrix is an antenna groupselection matrix and wherein the second type precoding matrix is a DFTmatrix.

Preferably, the second type precoding matrix includes a code in whichthe two components corresponding to the first antenna group and the twocomponents corresponding to the second antenna group are mutuallyorthogonal.

Preferably, the 4-antenna codebook includes a precoding matrix, in whichtwo components corresponding to either the first antenna group or thesecond antenna group are 0 in a first column and two componentscorresponding to either the second antenna group or the first antennagroup are 0 in a second column, for a rank 2.

More preferably, the 4-antenna codebook includes at least one selectedfrom the group consisting of a precoding matrix for performing a layerswapping function of changing positions of two layer signals and anantenna permutation precoding matrix for changing a position of anantenna, for the rank 2.

In another aspect of the present invention, a method of transmitting asignal, which is transmitted to a base station by a user equipment using4 antennas, includes the steps of obtaining transmission rankinformation, outputting a precoded signal by selecting one precodingmatrix corresponding to the transmission rank from a 4-antenna codebookincluding a first type precoding matrix of 4*3 matrix type including 2non-zero components in each row for a rank 3 and 2 zero components infirst and second columns and then performing precoding on layer signalsof which number corresponds to the transmission rank and transmittingthe precoded signal to the base station.

Preferably, the first type precoding matrix has a type of

${W_{N_{t} \times 3}^{n} = \begin{bmatrix}{\overset{\_}{v}}_{i} & \overset{\_}{z} & {\overset{\_}{v}}_{k} \\\overset{\_}{z} & {\overset{\_}{v}}_{j} & v_{l}\end{bmatrix}},$ν _(i), ν _(k), ν _(j) and ν _(l) are 2*1 vectors including non-zerocomponents only, and z is 2*1 vector including zero components only.

More preferably, the ν _(i) and the ν _(k) are mutually orthogonal andthe ν _(j) and the ν _(l) are mutually orthogonal. In this case, if anormalization coefficient for the ν _(i) and the ν _(j) is set to1/√{square root over (α)} and a normalization coefficient for the ν _(k)and the ν _(l) is set to 1/√{square root over (β)}, it meets α=2β. If anormalization coefficient for the ν _(i) and the ν _(j) is set to1/√{square root over (α)} and a normalization coefficient for the ν _(k)and the ν _(l) is set to 1/√{square root over (β)}, it meets α=β.

Preferably, the first type precoding matrix has a type resulting frommultiplying

$W_{N_{t} \times 3}^{n} = {\begin{bmatrix}1 & 0 & 1 \\{\mathbb{e}}^{{j\theta}_{1}} & 0 & {- {\mathbb{e}}^{{j\theta}_{1}}} \\0 & 1 & 1 \\0 & {\mathbb{e}}^{{j\theta}_{2}} & {- {\mathbb{e}}^{{j\theta}_{2}}}\end{bmatrix}\mspace{14mu}{or}}$$W_{N_{t} \times 3}^{n} = \begin{bmatrix}1 & 0 & 1 \\{- {\mathbb{e}}^{{j\theta}_{1}}} & 0 & {\mathbb{e}}^{{j\theta}_{1}} \\0 & {\mathbb{e}}^{{j\theta}_{2}} & {\mathbb{e}}^{{j\theta}_{2}} \\0 & {- {\mathbb{e}}^{{j\theta}_{3}}} & {\mathbb{e}}^{{j\theta}_{3}}\end{bmatrix}$by a normalization coefficient, the N_(t) is 4, the θ₁, θ₂ meet acondition of

${\theta_{2} \in \left\{ {{\frac{2\pi}{N}i},{i = 0},\ldots\mspace{14mu},{N - 1}} \right\}},$and the N is set to 4 or 8.

Preferably, the 4-antenna codebook further includes a second typeprecoding matrix of a 4*3 type including one non-zero component in eachrow.

More preferably, the second type precoding matrix has a type resultingfrom multiplying

$W_{N_{t} \times 3}^{n} = \begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1 \\0 & 0 & {\mathbb{e}}^{j\theta}\end{bmatrix}$by a normalization coefficient, the N_(t) is 4, the θ meets a conditionof

${\theta \in \left\{ {{\frac{2\pi}{N}i},{i = 0},\ldots\mspace{14mu},{N - 1}} \right\}},$and the N is set to 4 or 8. In this case, the second type precodingmatrix has a type multiplied by either a coefficient for inter-antennapower normalization or inter-layer power normalization.

In another aspect of the present invention, a method of receiving asignal, which is received by a base station from a user equipmentconfigured to use 4 antennas, includes the steps of receiving areception signal from the user equipment, obtaining transmission rankand precoding matrix identification information used by the userequipment for the reception signal transmission, and performing reverseprocessing of precoding on the reception signal by selecting oneprecoding matrix corresponding to the transmission rank and precodingmatrix identification information from a 4-antenna codebook, wherein the4 antennas are grouped into a first antenna group including two of the 4antennas and a second antenna group including the rest of the 4 antennasand wherein the 4-antenna codebook includes a first type precodingmatrix, in which two components corresponding to the first antenna groupare zero and two components corresponding to the second antenna groupconstruct a DFT matrix, and a second type precoding matrix, in which twocomponents corresponding to the first antenna group and two componentscorresponding to the second antenna group construct DFT matrixes,respectively, for a rank 1.

In another aspect of the present invention, a method of receiving asignal, which is received by a base station from a user equipment using4 antennas, includes the steps of receiving a reception signal from theuser equipment, obtaining transmission rank and precoding matrixidentification information used by the user equipment for the receptionsignal transmission, and performing reverse processing of precoding onthe reception signal by selecting one precoding matrix corresponding tothe transmission rank and precoding matrix identification informationfrom a 4-antenna codebook including a first type precoding matrix of 4*3matrix type including 2 non-zero components in each row for a rank 3 and2 zero components in first and second columns.

In another aspect of the present invention, a user equipment includes afirst antenna group including a first antenna and a second antenna, asecond antenna group including a third antenna and a fourth antenna, amemory configured to store a 4-antenna codebook including a first typeprecoding matrix, in which two components corresponding to the firstantenna group are zero and two components corresponding to the secondantenna group construct a DFT matrix, and a second type precodingmatrix, in which two components corresponding to the first antenna groupand two components corresponding to the second antenna group constructDFT matrixes, respectively, for a rank 1, and a precoder outputting asignal precoded by selecting one precoding matrix corresponding to atransmission rank from the 4-antenna codebook stored in the memory andthen performing precoding on layer signals of which number correspondsto the transmission rank, wherein the signal precoded by the precoder istransmitted to a base station via at least one selected from the groupconsisting of the first antenna group and the second antenna group.

In another aspect of the present invention, a user equipment includes amemory configured to store a 4-antenna codebook including a first typeprecoding matrix of 4*3 matrix type including 2 non-zero components ineach row for a rank 3 and 2 zero components in first and second columns,a precoder outputting a precoded signal by selecting one precodingmatrix corresponding to the transmission rank from the 4-antennacodebook, the precoder performing precoding on layer signals of whichnumber corresponds to the transmission rank, and four antennasconfigured to transmit the signal precoded by the precoder to a basestation.

In another aspect of the present invention, a base station includes anantenna configured to receive a reception signal transmitted from a userequipment configured to transmit a signal using four antennas groupedinto a first antenna group including two of the 4 antennas and a secondantenna group including the rest of the 4 antennas, a memory configuredto store a 4-antenna codebook including a first type precoding matrix,in which two components corresponding to the first antenna group arezero and two components corresponding to the second antenna groupconstruct a DFT matrix, and a second type precoding matrix, in which twocomponents corresponding to the first antenna group and two componentscorresponding to the second antenna group construct DFT matrixes,respectively, for a rank 1, and a precoder performing reverse processingof precoding on the reception signal by selecting one precoding matrixcorresponding to transmission rank and precoding matrix identificationinformation used by the user equipment from the 4-antenna codebook.

In another aspect of the present invention, a base station includes anantenna configured to receive a reception signal transmitted from a userequipment configured to use four antennas, a memory configured to storea 4-antenna codebook including a first type precoding matrix of 4*3matrix type including 2 non-zero components in each row for a rank 3 and2 zero components in first and second columns, and a precoder performingreverse processing of precoding on the reception signal received via theantenna by selecting one precoding matrix corresponding to transmissionrank and precoding matrix identification information used by the userequipment from the 4-antenna codebook stored in the memory.

Besides, it is apparent that the above-mentioned embodiments for therank 1, rank 2 and rank 3 of the 4-antenna codebook are usable in amanner of being combined into a type including a prescribed number ofprecoding matrixes for each of the ranks in one codebook.

Accordingly, the present invention provides the following effects and/oradvantages.

First of all, if a codebook according to one of embodiments of thepresent invention is used, it is able to efficiently perform atransmission control per antenna group.

Secondly, in uplink signal transmission, the present invention is ableto maintain a sensitive PAPR/CM property well.

Effects attainable from the embodiments of the present invention arenon-limited to the above-mentioned effects. Other unmentioned effectscan be clearly derived and understood from the description of thefollowing embodiments of the present invention by those having ordinaryskill in the art to which the present invention pertains. Namely,effects unintended in the application stage of the present invention canbe derived from the embodiments of the present invention by those havingordinary skill in the art to which the present invention pertains.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are included to provide a furtherunderstanding of the invention and are incorporated in and constitute apart of this application, illustrate embodiment(s) of the invention andtogether with the description serve to explain the principle of theinvention. In the drawings:

FIG. 1 is a diagram for explaining a basic concept of codebook basedprecoding;

FIG. 2 is a diagram for explaining ULA antenna setup and X-pol antennasetup;

FIG. 3 is a diagram for explaining general SC-FDMA;

FIG. 4 is a diagram for detailed configuration of a processor of a userequipment according to one embodiment of the present invention; and

FIG. 5 is a diagram for configurations of a base station and a userequipment.

DETAILED DESCRIPTION OF THE INVENTION

Reference will now be made in detail to the preferred embodiments of thepresent invention, examples of which are illustrated in the accompanyingdrawings. In the following detailed description of the inventionincludes details to help the full understanding of the presentinvention. Yet, it is apparent to those skilled in the art that thepresent invention can be implemented without these details. Forinstance, the following description is made with reference topredetermined terminologies, by which the present invention isnon-limited. Even if an arbitrary terminology is used, it can have thesame meaning of the predetermined terminology. Wherever possible, thesame reference numbers will be used throughout the drawings to refer tothe same or like parts.

In the following description, ‘rank’ indicates the number of paths forcarrying signals independently and ‘the number of layers’ indicates thenumber of signal streams transmitted via each path. Generally, as atransmitting side transmits layers of which number corresponds to therank number used for signal transmission, a rank has the same meaning ofthe layer number (i.e., the number of layers) unless there is a specialnote. In a precoding matrix, assume that a row corresponds to eachantenna and that a column corresponds to a rank or each layer signal.

Table 1 shows 4-antenna codebook structure in LTE release 8.

TABLE 1 Codebook Number of layers υ index u_(n) 1 2 3 4 0 u₀ = [1 −1 −1−1]^(T) W₀ ^({1}) W₀ ^({14})/{square root over (2)} W₀ ^({124})/{squareroot over (3)} W₀ ^({1234})/2 1 u₁ = [1 −j 1 j]^(T) W₁ ^({1}) W₁^({12})/{square root over (2)} W₁ ^({123})/{square root over (3)} W₁^({1234})/2 2 u₂ = [1 1 −1 1]^(T) W₂ ^({1}) W₂ ^({12})/{square root over(2)} W₂ ^({123})/{square root over (3)} W₂ ^({3214})/2 3 u₃ = [1 j 1−j]^(T) W₃ ^({1}) W₃ ^({12})/{square root over (2)} W₃ ^({123})/{squareroot over (3)} W₃ ^({3214})/2 4 u₄ = [1 (−1 − j)/{square root over (2)}−j (1 − j)/{square root over (2)}]^(T) W₄ ^({1}) W₄ ^({14})/{square rootover (2)} W₄ ^({124})/{square root over (3)} W₄ ^({1234})/2 5 u₅ = [1 (1− j)/{square root over (2)} j (−1 − j)/{square root over (2)}]^(T) W₅^({1}) W₅ ^({14})/{square root over (2)} W₅ ^({124})/{square root over(3)} W₅ ^({1234})/2 6 u₆ = [1 (1 + j)/{square root over (2)} −j (−1 +j)/{square root over (2)}]^(T) W₆ ^({1}) W₆ ^({13})/{square root over(2)} W₆ ^({134})/{square root over (3)} W₆ ^({1324})/2 7 u₇ = [1 (−1 +j)/{square root over (2)} j (1 + j)/{square root over (2)}]^(T) W₇^({1}) W₇ ^({13})/{square root over (2)} W₇ ^({134})/{square root over(3)} W₇ ^({1324})/2 8 u₈ = [1 −1 1 1]^(T) W₈ ^({1}) W₈ ^({12})/{squareroot over (2)} W₈ ^({124})/{square root over (3)} W₈ ^({1234})/2 9 u₉ =[1 −j −1 −j]^(T) W₉ ^({1}) W₉ ^({14})/{square root over (2)} W₉^({134})/{square root over (3)} W₉ ^({1234})/2 10 u₁₀ = [1 1 1 −1]^(T)W₁₀ ^({1}) W₁₀ ^({13})/{square root over (2)} W₁₀ ^({123})/{square rootover (3)} W₁₀ ^({1324})/2 11 u₁₁ = [1 j −1 j]^(T) W₁₁ ^({1}) W₁₁^({13})/{square root over (2)} W₁₁ ^({134})/{square root over (3)} W₁₁^({1324})/2 12 u₁₂ = [1 −1 −1 1]^(T) W₁₂ ^({1}) W₁₂ ^({12})/{square rootover (2)} W₁₂ ^({123})/{square root over (3)} W₁₂ ^({1234})/2 13 u₁₃ =[1 −1 1 −1]^(T) W₁₃ ^({1}) W₁₃ ^({13})/{square root over (2)} W₁₃^({123})/{square root over (3)} W₁₃ ^({1324})/2 14 u₁₄ = [1 1 −1 −1]^(T)W₁₄ ^({1}) W₁₄ ^({13})/{square root over (2)} W₁₄ ^({123})/{square rootover (3)} W₁₄ ^({3214})/2 15 u₁₅ = [1 1 1 1]^(T) W₁₅ ^({1}) W₁₅^({12})/{square root over (2)} W₁₅ ^({123})/{square root over (3)} W₁₅^({1234})/2

In Table 1, W_(n) ^({s}) can be prescribed as W_(n)=I−2u_(n)u_(n)^(H)/u_(n) ^(H)u_(n) for a set including a column indicated by {s}. Inthis case, I indicates 4*4 identity matrix. Referring to Table 1, 4-Txcodebook prescribed in LTE release 8 is constructed with total 64precoding matrixes including 16 precoding matrixes for each rank. Thecodebook shown in Table 1 has the following properties.

-   -   Constant modulus property: each component of each precoding        vector/matrix has uniform power.    -   Nested property: a precoding vector/matrix at a low rank is        included in a column of a precoding vector/matrix of a high        rank.    -   Limited number of components: component (precoding alphabet) of        precoding matrix is limited to

$\left\{ {{\pm 1},{\pm j},{\pm \frac{\left( {1 + j} \right)}{\sqrt{2}}},{\pm \frac{\left( {{- 1} + j} \right)}{\sqrt{2}}}} \right\}.$

In consideration of the above mentioned features, a codebook structurefor uplink signal transmission in LTE-A system is explained as follows.

FIG. 2 is a diagram for explaining ULA antenna setup and X-pol antennasetup.

The codebook structure shown in Table 1 is designed in consideration ofULA (uniform linear array) antenna setup shown in a left part of FIG. 2.Generally, the ULA antenna type needs a big antenna space to maintainantenna correlation over a predetermined level. Accordingly, in order touse a number of antennas like 4Tx, 8Tx or the like, a cross-pol (X-pol)antenna setup shown in a right part of FIG. 2 is used. In case of theX-pol antenna setup, it is able to reduce an antenna space smaller thanthat of the ULA antenna setup. Therefore, the X-pol antenna setup istaken into consideration in designing 4-Tx system codebook for LTE-A.

A precoding matrix can be represented as N_(t)×R matrix. In this case,N_(t) indicates the number of antennas and R indicates a rank. Acodebook for the rank R can be represented as W_(N) _(t) _(×R) ^(i),i=0, . . . , N_(rank). In this case, N_(rank) indicates the number ofprecoding matrixes for the rank R.

According to one embodiment of the present invention, N_(t) antennas canbe divided into at least two groups. For instance, antenna port 1 andantenna port 3 can be grouped into one antenna group in the setup shownin the right part of FIG. 2, while antenna port 2 and antenna port 4 canbe grouped into another antenna group in the setup shown in the rightpart of FIG. 2.

A recoding matrix can be designed to be suitable for each of theabove-mentioned antennas groups. For instance, 2Tx codebook is usablefor each of the above-mentioned antenna groups and is also usable bybeing combined for 4Tx codebook. In order to completely separate thesetwo antenna groups from each other, one embodiment of the presentinvention proposes to use a zero vector/matrix. If 4Tx system includestwo antenna groups each of which includes two antennas, Table 2 showsvectors/matrixes usable for each of the antenna groups.

TABLE 2 Number of layers Precoding Zero υ vectors/matrices vector/matrix1 $\underset{\underset{{\overset{\_}{v}}_{1}}{︸}}{\begin{bmatrix}v_{1}^{1} \\v_{1}^{2}\end{bmatrix}},\underset{\underset{{\overset{\_}{v}}_{2}}{︸}}{\begin{bmatrix}v_{2}^{1} \\v_{2}^{2}\end{bmatrix}},\underset{\underset{{\overset{\_}{v}}_{3}}{︸}}{\begin{bmatrix}v_{3}^{1} \\v_{3}^{2}\end{bmatrix}},\underset{\underset{{\overset{\_}{v}}_{4}}{︸}}{\begin{bmatrix}v_{4}^{1} \\v_{4}^{2}\end{bmatrix}}$$\underset{\overset{\_}{z}}{\underset{︸}{\begin{bmatrix}0 \\0\end{bmatrix}}}$ 2 $\underset{\underset{w}{︸}}{\begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}}$ $\underset{\underset{z}{︸}}{\begin{bmatrix}0 & 0 \\0 & 0\end{bmatrix}}$

In Table 2, ν_(i) ^(j), i=1, . . . , 4, j=1, 2, indicates a complexnumber value having a unit power. If a component of each precodingmatrix is limited to {±1, ±j}, precoding vector/matrix candidates foreach antenna group can be represented as follows.

TABLE 3 Number of layers Precoding Zero υ vectors/matrices vector/matrix1 $\underset{\underset{{\overset{\_}{v}}_{1}}{︸}}{\begin{bmatrix}1 \\1\end{bmatrix}},\underset{\underset{{\overset{\_}{v}}_{2}}{︸}}{\begin{bmatrix}1 \\{- 1}\end{bmatrix}},\underset{\underset{{\overset{\_}{v}}_{3}}{︸}}{\begin{bmatrix}1 \\j\end{bmatrix}},\underset{\underset{{\overset{\_}{v}}_{4}}{︸}}{\begin{bmatrix}1 \\{- j}\end{bmatrix}}$$\underset{\overset{\_}{z}}{\underset{︸}{\begin{bmatrix}0 \\0\end{bmatrix}}}$ 2 $\underset{\underset{w}{︸}}{\begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}}$ $\underset{\underset{z}{︸}}{\begin{bmatrix}0 & 0 \\0 & 0\end{bmatrix}}$

According to another embodiment of the present invention, it is able todesign a codebook using the following precoding vector/matrixcandidates.

TABLE 4 Precoding Number of layers υ vectors/matrices Zero vector/matrix1 $\underset{{\overset{\_}{v}}_{1}}{\underset{︸}{\begin{bmatrix}1 \\1\end{bmatrix}}},\underset{{\overset{\_}{v}}_{2}}{\underset{︸}{\begin{bmatrix}1 \\{- 1}\end{bmatrix}}},\underset{{\overset{\_}{v}}_{3}}{\underset{︸}{\begin{bmatrix}1 \\j\end{bmatrix}}},\underset{{\overset{\_}{v}}_{4}}{\underset{︸}{\begin{bmatrix}1 \\{- j}\end{bmatrix}}}$$\underset{\overset{\_}{z}}{\underset{︸}{\begin{bmatrix}0 \\0\end{bmatrix}}},\underset{{\overset{\_}{\gamma}}_{1}}{\underset{︸}{\begin{bmatrix}0 \\1\end{bmatrix}}},\underset{{\overset{\_}{\gamma}}_{2}}{\underset{︸}{\begin{bmatrix}1 \\0\end{bmatrix}}}$

In Table 3 and Table 4, matrixes except zero vector/matrix can be calledDFT matrixes. In the following description, 4Tx uplink codebook isdescribed in detail per rank.

Rank-1 Codebook

First of all, it is able to design a rank-1 precoding matrix of 4Txsystem by combining two vectors/matrixes for 1 layer in Table 3 or Table4 in one column.

Total combinations of precoding vectors/matrixes per antenna except zerovector/matrix in Table 3 or Table 4 can be represented as follows.

TABLE 5 Number of layers υ Layer-1 codebook (W^(n) _(N×1)) 1$\begin{matrix}{\quad{\begin{bmatrix}{\overset{\_}{v}}_{1} \\{\overset{\_}{v}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{1} \\{\overset{\_}{v}}_{2}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{1} \\{\overset{\_}{v}}_{3}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{1} \\{\overset{\_}{v}}_{4}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{2} \\{\overset{\_}{v}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{2} \\{\overset{\_}{v}}_{2}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{2} \\{\overset{\_}{v}}_{3}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{2} \\{\overset{\_}{v}}_{4}\end{bmatrix},}\;} \\{{{\begin{bmatrix}{\overset{\_}{v}}_{3} \\{\overset{\_}{v}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{3} \\{\overset{\_}{v}}_{2}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{3} \\{\overset{\_}{v}}_{3}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{3} \\{\overset{\_}{v}}_{4}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{4} \\{\overset{\_}{v}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{4} \\{\overset{\_}{v}}_{2}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{4} \\{\overset{\_}{v}}_{3}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{4} \\{\overset{\_}{v}}_{4}\end{bmatrix}}\quad}{\quad\quad}}\end{matrix}\quad$

Meanwhile, it is able to design a codebook in consideration of antennapermutation. In this case, it is able to permutate all precodingvectors/matrixes within the codebook using the same antenna permutationmatrix Π. According to this embodiment, the precoding matrixes shown inTable 5 can be represented as follows using a permutation matrix.Π·W _(N) _(t) _(×1) , n=0, . . . , N _(c)−1  [Formula 1]

In Formula 1, N_(c) indicates the number of precoding vectors/matrixesper layer. The above-described permutation matrix can be represented asfollows.

TABLE 6 Π Π₁ $\begin{bmatrix}1 & 0 & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 0 & 1\end{bmatrix}\quad$ Π₂ $\begin{bmatrix}1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 0 & 1 & 0\end{bmatrix}\quad$ Π₃ $\begin{bmatrix}1 & 0 & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}\quad$ Π₄ $\begin{bmatrix}1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0 \\0 & 0 & 1 & 0\end{bmatrix}\quad$ Π₅ $\begin{bmatrix}1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 \\0 & 1 & 0 & 0\end{bmatrix}\quad$ Π₆ $\begin{bmatrix}0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & 1\end{bmatrix}\quad$ Π₇ $\begin{bmatrix}0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 0 & 1 & 0\end{bmatrix}\quad$ Π₈ $\begin{bmatrix}0 & 1 & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & 1 \\1 & 0 & 0 & 0\end{bmatrix}\quad$ Π₉ $\begin{bmatrix}0 & 1 & 0 & 0 \\0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1\end{bmatrix}\quad$ Π₁₀ $\begin{bmatrix}0 & 1 & 0 & 0 \\0 & 0 & 0 & 1 \\1 & 0 & 0 & 0 \\0 & 0 & 1 & 0\end{bmatrix}\quad$ Π₁₁ $\begin{bmatrix}0 & 1 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 \\1 & 0 & 0 & 0\end{bmatrix}\quad$ Π₁₂ $\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 0 & 1\end{bmatrix}\quad$ Π₁₃ $\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}\quad$ Π₁₄ $\begin{bmatrix}0 & 0 & 1 & 0 \\0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1\end{bmatrix}\quad$ Π₁₅ $\begin{bmatrix}0 & 0 & 1 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 0 & 1 \\1 & 0 & 0 & 0\end{bmatrix}\quad$ Π₁₆ $\begin{bmatrix}0 & 0 & 1 & 0 \\0 & 0 & 0 & 1 \\1 & 0 & 0 & 0 \\0 & 1 & 0 & 0\end{bmatrix}\quad$ Π₁₇ $\begin{bmatrix}0 & 0 & 1 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0 \\1 & 0 & 0 & 0\end{bmatrix}\quad$ Π₁₈ $\begin{bmatrix}0 & 0 & 0 & 1 \\1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 1 & 0\end{bmatrix}\quad$ Π₁₉ $\begin{bmatrix}0 & 0 & 0 & 1 \\1 & 0 & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 1 & 0 & 0\end{bmatrix}\quad$ Π₂₀ $\begin{bmatrix}0 & 0 & 0 & 1 \\0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 1 & 0\end{bmatrix}\quad$ Π₂₁ $\begin{bmatrix}0 & 0 & 0 & 1 \\0 & 1 & 0 & 0 \\0 & 0 & 1 & 0 \\1 & 0 & 0 & 0\end{bmatrix}\quad$ Π₂₂ $\begin{bmatrix}0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 1 & 0 & 0\end{bmatrix}\quad$ Π₂₃ $\begin{bmatrix}0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 \\0 & 1 & 0 & 0 \\1 & 0 & 0 & 0\end{bmatrix}\quad$

For clarity of the following description, assume that Π₁ is used as apermutation matrix. Yet, other permutation matrixes are available aswell.

If the precoding vector/matrix per antenna shown in Table 4 is appliedto Table 5, it is able to configure the following rank-1 (layer-1)codebook.

TABLE 7 Number of layers υ Layer-1 codebook (W^(n) _(N) _(t) _(×1)) 1$\begin{matrix}{{\quad\begin{bmatrix}1 \\1 \\1 \\1\end{bmatrix}},\begin{bmatrix}1 \\1 \\1 \\{- 1}\end{bmatrix},\begin{bmatrix}1 \\1 \\1 \\j\end{bmatrix},\begin{bmatrix}1 \\1 \\1 \\{- j}\end{bmatrix},\begin{bmatrix}1 \\{- 1} \\1 \\1\end{bmatrix},\begin{bmatrix}1 \\{- 1} \\1 \\{- 1}\end{bmatrix},\begin{bmatrix}1 \\{- 1} \\1 \\j\end{bmatrix},\begin{bmatrix}1 \\{- 1} \\1 \\{- j}\end{bmatrix},} \\{\begin{bmatrix}1 \\j \\1 \\1\end{bmatrix},\begin{bmatrix}1 \\j \\1 \\{- 1}\end{bmatrix},\begin{bmatrix}1 \\j \\1 \\j\end{bmatrix},\begin{bmatrix}1 \\j \\1 \\{- j}\end{bmatrix},\begin{bmatrix}1 \\{- j} \\1 \\1\end{bmatrix},\begin{bmatrix}1 \\{- j} \\1 \\{- 1}\end{bmatrix},\begin{bmatrix}1 \\{- j} \\1 \\j\end{bmatrix},\begin{bmatrix}1 \\{- j} \\1 \\{- j}\end{bmatrix}}\end{matrix}\quad$

Moreover, if a permutation using antenna permutation matrix Π₁ isadditionally taken into consideration for Table 7, it is able to designthe following rank-1 codebook.

TABLE 8 Number of layers υ Layer-1 codebook (Π· W^(n) _(N) _(t) _(×1)) 1$\begin{matrix}{{\quad\begin{bmatrix}1 \\1 \\1 \\1\end{bmatrix}},\begin{bmatrix}1 \\1 \\1 \\{- 1}\end{bmatrix},\begin{bmatrix}1 \\1 \\1 \\j\end{bmatrix},\begin{bmatrix}1 \\1 \\1 \\{- j}\end{bmatrix},\begin{bmatrix}1 \\1 \\{- 1} \\1\end{bmatrix},\begin{bmatrix}1 \\1 \\{- 1} \\{- 1}\end{bmatrix},\begin{bmatrix}1 \\1 \\{- 1} \\j\end{bmatrix},\begin{bmatrix}1 \\1 \\{- 1} \\{- j}\end{bmatrix},} \\{\begin{bmatrix}1 \\1 \\j \\1\end{bmatrix},\begin{bmatrix}1 \\1 \\j \\{- 1}\end{bmatrix},\begin{bmatrix}1 \\1 \\j \\j\end{bmatrix},\begin{bmatrix}1 \\1 \\j \\{- j}\end{bmatrix},\begin{bmatrix}1 \\1 \\{- j} \\1\end{bmatrix},\begin{bmatrix}1 \\1 \\{- j} \\{- 1}\end{bmatrix},\begin{bmatrix}1 \\1 \\{- j} \\j\end{bmatrix},\begin{bmatrix}1 \\1 \\{- j} \\{- j}\end{bmatrix}}\end{matrix}\quad$

According to another embodiment of the present invention, only part ofprecoding matrixes in the rank-1 codebook can be configured in a typethat uses a permutation matrix as follows.

TABLE 9 Number of layers ν Layer-1 codebook (W_(N) _(t) _(×1) ^(n)) 1$\begin{bmatrix}{\overset{\_}{v}}_{1} \\{\overset{\_}{v}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{1} \\{\overset{\_}{v}}_{2}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{2} \\{\overset{\_}{v}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{2} \\{\overset{\_}{v}}_{2}\end{bmatrix},$ $\begin{bmatrix}{\overset{\_}{v}}_{3} \\{\overset{\_}{v}}_{3}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{3} \\{\overset{\_}{v}}_{4}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{4} \\{\overset{\_}{v}}_{3}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{4} \\{\overset{\_}{v}}_{4}\end{bmatrix},$ ${\Pi\begin{bmatrix}{\overset{\_}{v}}_{1} \\{\overset{\_}{v}}_{1}\end{bmatrix}},{\Pi\begin{bmatrix}{\overset{\_}{v}}_{1} \\{\overset{\_}{v}}_{2}\end{bmatrix}},{\Pi\begin{bmatrix}{\overset{\_}{v}}_{2} \\{\overset{\_}{v}}_{1}\end{bmatrix}},{\Pi\begin{bmatrix}{\overset{\_}{v}}_{2} \\{\overset{\_}{v}}_{2}\end{bmatrix}},$ ${\Pi\begin{bmatrix}{\overset{\_}{v}}_{3} \\{\overset{\_}{v}}_{3}\end{bmatrix}},{\Pi\begin{bmatrix}{\overset{\_}{v}}_{3} \\{\overset{\_}{v}}_{4}\end{bmatrix}},{\Pi\begin{bmatrix}{\overset{\_}{v}}_{4} \\{\overset{\_}{v}}_{3}\end{bmatrix}},{\Pi\begin{bmatrix}{\overset{\_}{v}}_{4} \\{\overset{\_}{v}}_{4}\end{bmatrix}}$

TABLE 10 Number of layers ν Layer-1 codebook (W_(N) _(t) _(×1) ^(n)) 1$\begin{bmatrix}{\overset{\_}{v}}_{1} \\{\overset{\_}{v}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{1} \\{\overset{\_}{v}}_{2}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{1} \\{\overset{\_}{v}}_{3}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{1} \\{\overset{\_}{v}}_{4}\end{bmatrix},$ $\begin{bmatrix}{\overset{\_}{v}}_{2} \\{\overset{\_}{v}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{2} \\{\overset{\_}{v}}_{2}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{2} \\{\overset{\_}{v}}_{3}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{2} \\{\overset{\_}{v}}_{4}\end{bmatrix},$ $\begin{bmatrix}{\overset{\_}{v}}_{3} \\{\overset{\_}{v}}_{3}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{3} \\{\overset{\_}{v}}_{4}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{4} \\{\overset{\_}{v}}_{3}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{4} \\{\overset{\_}{v}}_{4}\end{bmatrix},$ ${\Pi\begin{bmatrix}{\overset{\_}{v}}_{3} \\{\overset{\_}{v}}_{3}\end{bmatrix}},{\Pi\begin{bmatrix}{\overset{\_}{v}}_{3} \\{\overset{\_}{v}}_{4}\end{bmatrix}},{\Pi\begin{bmatrix}{\overset{\_}{v}}_{4} \\{\overset{\_}{v}}_{3}\end{bmatrix}},{\Pi\begin{bmatrix}{\overset{\_}{v}}_{4} \\{\overset{\_}{v}}_{4}\end{bmatrix}}$

Meanwhile, according to one preferred embodiment of the presentinvention, proposed is a method of designing a codebook to have amutually orthogonal property between vectors/matrixes corresponding toeach antenna group in a precoding matrix within a codebook. Table 11shows an example for configuring a codebook by selecting precodingmatrixes meeting the mutually orthogonal property between thecorresponding antenna groups shown in Table 5.

TABLE 11 Number of layers ν Layer-1 codebook (W_(N) _(t) _(×1) ^(n)) 1$\begin{bmatrix}{\overset{\_}{v}}_{1} \\{\overset{\_}{v}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{2} \\{\overset{\_}{v}}_{2}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{3} \\{\overset{\_}{v}}_{3}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{4} \\{\overset{\_}{v}}_{4}\end{bmatrix},$ ${\Pi\begin{bmatrix}{\overset{\_}{v}}_{1} \\{\overset{\_}{v}}_{1}\end{bmatrix}},{\Pi\begin{bmatrix}{\overset{\_}{v}}_{2} \\{\overset{\_}{v}}_{2}\end{bmatrix}},{\Pi\begin{bmatrix}{\overset{\_}{v}}_{3} \\{\overset{\_}{v}}_{3}\end{bmatrix}},{\Pi\begin{bmatrix}{\overset{\_}{v}}_{4} \\{\overset{\_}{v}}_{4}\end{bmatrix}},$

Meanwhile, according to one embodiment of the present invention,proposed is a method of configuring a codebook that includes an antennagroup selection matrix. In particular, in case that 4 antennas aregrouped into a first antenna group including 2 of the 4 antennas and asecond antenna group including the rest, the codebook is designed in amanner that 2 components corresponding to one of the antenna groups areset to 0 and that 2 components corresponding to the other antenna groupconstruct a DFT matrix. Through this, it is able to turn off antennas byan antenna group unit at a timing point of transmitting an uplink signalto a base station from a user equipment.

Table 12 shows an example of the above-described antenna group selectionmatrix.

TABLE 12 Number of layers ν Layer-1 codebook (W_(N) _(t) _(×1) ^(n)) 1$\begin{bmatrix}{\overset{\_}{v}}_{1} \\z\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{2} \\z\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{3} \\z\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{4} \\z\end{bmatrix},$ $\begin{bmatrix}z \\{\overset{\_}{v}}_{1}\end{bmatrix},\begin{bmatrix}z \\{\overset{\_}{v}}_{2}\end{bmatrix},\begin{bmatrix}z \\{\overset{\_}{v}}_{3}\end{bmatrix},\begin{bmatrix}z \\{\overset{\_}{v}}_{4}\end{bmatrix},$ ${\Pi\begin{bmatrix}{\overset{\_}{v}}_{1} \\z\end{bmatrix}},{\Pi\begin{bmatrix}{\overset{\_}{v}}_{2} \\z\end{bmatrix}},{\Pi\begin{bmatrix}{\overset{\_}{v}}_{3} \\z\end{bmatrix}},{\Pi\begin{bmatrix}{\overset{\_}{v}}_{4} \\z\end{bmatrix}},$ ${\Pi\begin{bmatrix}z \\{\overset{\_}{v}}_{1}\end{bmatrix}},{\Pi\begin{bmatrix}z \\{\overset{\_}{v}}_{2}\end{bmatrix}},{\Pi\begin{bmatrix}z \\{\overset{\_}{v}}_{3}\end{bmatrix}},{\Pi\begin{bmatrix}z \\{\overset{\_}{v}}_{4}\end{bmatrix}}$

According to a preferred embodiment of the present invention, proposedis a method of configuring 4Tx rank-1 codebook in a manner that thecorresponding codebook includes both of the antenna group selectionmatrix shown in Table 12 and the DFT matrix shown in Table 5. Table 13and Table 14 are examples for the 4Tx rank-1 codebook according to thisembodiment.

TABLE 13 Number of layers ν Layer-1 codebook (W_(N) _(t) _(×1) ^(n)) 1$\begin{bmatrix}{\overset{\_}{v}}_{1} \\z\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{2} \\z\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{3} \\z\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{4} \\z\end{bmatrix},$ $\begin{bmatrix}z \\{\overset{\_}{v}}_{1}\end{bmatrix},\begin{bmatrix}z \\{\overset{\_}{v}}_{2}\end{bmatrix},\begin{bmatrix}z \\{\overset{\_}{v}}_{3}\end{bmatrix},\begin{bmatrix}z \\{\overset{\_}{v}}_{4}\end{bmatrix},$ $\begin{bmatrix}{\overset{\_}{v}}_{1} \\{\overset{\_}{v}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{1} \\{\overset{\_}{v}}_{2}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{2} \\{\overset{\_}{v}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{2} \\{\overset{\_}{v}}_{2}\end{bmatrix},$ $\begin{bmatrix}{\overset{\_}{v}}_{3} \\{\overset{\_}{v}}_{3}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{3} \\{\overset{\_}{v}}_{4}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{4} \\{\overset{\_}{v}}_{3}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{4} \\{\overset{\_}{v}}_{4}\end{bmatrix}$

TABLE 14 Number of layers ν Layer-1 codebook (W_(N) _(t) _(×1) ^(n)) 1$\begin{bmatrix}{\overset{\_}{v}}_{1} \\z\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{2} \\z\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{3} \\z\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{4} \\z\end{bmatrix},$ ${\Pi\begin{bmatrix}{\overset{\_}{v}}_{1} \\z\end{bmatrix}},{\Pi\begin{bmatrix}{\overset{\_}{v}}_{2} \\z\end{bmatrix}},{\Pi\begin{bmatrix}{\overset{\_}{v}}_{3} \\z\end{bmatrix}},{\Pi\begin{bmatrix}{\overset{\_}{v}}_{4} \\z\end{bmatrix}}$ $\begin{bmatrix}{\overset{\_}{v}}_{1} \\{\overset{\_}{v}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{1} \\{\overset{\_}{v}}_{2}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{2} \\{\overset{\_}{v}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{2} \\{\overset{\_}{v}}_{2}\end{bmatrix},$ $\begin{bmatrix}{\overset{\_}{v}}_{3} \\{\overset{\_}{v}}_{3}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{3} \\{\overset{\_}{v}}_{4}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{4} \\{\overset{\_}{v}}_{3}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{4} \\{\overset{\_}{v}}_{4}\end{bmatrix}$

Rank-2 Codebook

According to one embodiment of the present invention, proposed is amethod of setting a rank-2 codebook to further include a precodingmatrix of a permutated type of the precoding matrix within the codebookshown in Table 15. In this case, if a used permutation matrix isrepresented as Π, a permutated precoding matrix can be represented asfollows.Π·W _(N) _(t) _(×2) ^(n) , n=0, . . . , N _(c)−1  [Formula 2]

The above permutation matrix can be selected from Table 6.

In case that Table 4 is used as a precoding vector/matrix for eachantenna group, Table 15 can be modified into Table 16.

TABLE 16 Number of layers ν Layer-2 codebook (W_(N) _(t) _(×2) ^(n))W_(N) _(t) _(×2) ⁰ W_(N) _(t) _(×2) ¹ W_(N) _(t) _(×2) ² W_(N) _(t)_(×2) ³ $\begin{bmatrix}1 & 0 \\1 & 0 \\0 & 1 \\0 & 1\end{bmatrix}\quad$ $\begin{bmatrix}1 & 0 \\1 & 0 \\0 & 1 \\0 & {- 1}\end{bmatrix}\quad$ $\begin{bmatrix}1 & 0 \\1 & 0 \\0 & 1 \\0 & j\end{bmatrix}\quad$ $\begin{bmatrix}1 & 0 \\1 & 0 \\0 & 1 \\0 & {- j}\end{bmatrix}\quad$ W_(N) _(t) _(×2) ⁴ W_(N) _(t) _(×2) ⁵ W_(N) _(t)_(×2) ⁶ W_(N) _(t) _(×2) ⁷ $\begin{bmatrix}1 & 0 \\{- 1} & 0 \\0 & 1 \\0 & 1\end{bmatrix}\quad$ $\begin{bmatrix}1 & 0 \\{- 1} & 0 \\0 & 1 \\0 & {- 1}\end{bmatrix}\quad$ $\begin{bmatrix}1 & 0 \\{- 1} & 0 \\0 & 1 \\0 & j\end{bmatrix}\quad$ $\begin{bmatrix}1 & 0 \\{- 1} & 0 \\0 & 1 \\0 & {- j}\end{bmatrix}\quad$ W_(N) _(t) _(×2) ⁸ W_(N) _(t) _(×2) ⁹ W_(N) _(t)_(×2) ¹⁰ W_(N) _(t) _(×2) ¹¹ $\begin{bmatrix}1 & 0 \\j & 0 \\0 & 1 \\0 & 1\end{bmatrix}\quad$ $\begin{bmatrix}1 & 0 \\j & 0 \\0 & 1 \\0 & {- 1}\end{bmatrix}\quad$ $\begin{bmatrix}1 & 0 \\j & 0 \\0 & 1 \\0 & j\end{bmatrix}\quad$ $\begin{bmatrix}1 & 0 \\j & 0 \\0 & 1 \\0 & {- j}\end{bmatrix}\quad$ W_(N) _(t) _(×2) ¹² W_(N) _(t) _(×2) ¹³ W_(N) _(t)_(×2) ¹⁴ W_(N) _(t) _(×2) ¹⁵ $\begin{bmatrix}1 & 0 \\{- j} & 0 \\0 & 1 \\0 & 1\end{bmatrix}\quad$ $\begin{bmatrix}1 & 0 \\{- j} & 0 \\0 & 1 \\0 & {- 1}\end{bmatrix}\quad$ $\begin{bmatrix}1 & 0 \\{- j} & 0 \\0 & 1 \\0 & j\end{bmatrix}\quad$ $\begin{bmatrix}1 & 0 \\{- j} & 0 \\0 & 1 \\0 & {- j}\end{bmatrix}\quad$

If a permutation matrix is applied to Table 16, a rank-2 codebook can berepresented as follows.

TABLE 17 Number of layers ν Layer-2 codebook (Π · W_(N) _(t) _(×2) ^(n))2 Π · Π · Π · Π · W_(N) _(t) _(×2) ⁰ W_(N) _(t) _(×2) ¹ W_(N) _(t) _(×2)² W_(N) _(t) _(×2) ³ $\begin{bmatrix}1 & 0 \\0 & 1 \\1 & 0 \\0 & 1\end{bmatrix}\quad$ $\begin{bmatrix}1 & 0 \\0 & 1 \\1 & 0 \\0 & {- 1}\end{bmatrix}\quad$ $\begin{bmatrix}1 & 0 \\0 & 1 \\1 & 0 \\0 & j\end{bmatrix}\quad$ $\begin{bmatrix}1 & 0 \\0 & 1 \\1 & 0 \\0 & {- j}\end{bmatrix}\quad$ Π · Π · Π · Π · W_(N) _(t) _(×2) ⁴ W_(N) _(t) _(×2)⁵ W_(N) _(t) _(×2) ⁶ W_(N) _(t) _(×2) ⁷ $\begin{bmatrix}1 & 0 \\0 & 1 \\{- 1} & 0 \\0 & 1\end{bmatrix}\quad$ $\begin{bmatrix}1 & 0 \\0 & 1 \\{- 1} & 0 \\0 & {- 1}\end{bmatrix}\quad$ $\begin{bmatrix}1 & 0 \\0 & 1 \\{- 1} & 0 \\0 & j\end{bmatrix}\quad$ $\begin{bmatrix}1 & 0 \\0 & 1 \\{- 1} & 0 \\0 & {- j}\end{bmatrix}\quad$ Π · Π · Π · Π · W_(N) _(t) _(×2) ⁸ W_(N) _(t) _(×2)⁹ W_(N) _(t) _(×2) ¹⁰ W_(N) _(t) _(×2) ¹¹ $\begin{bmatrix}1 & 0 \\0 & 1 \\j & 0 \\0 & 1\end{bmatrix}\quad$ $\begin{bmatrix}1 & 0 \\0 & 1 \\j & 0 \\0 & {- 1}\end{bmatrix}\quad$ $\begin{bmatrix}1 & 0 \\0 & 1 \\j & 0 \\0 & j\end{bmatrix}\quad$ $\begin{bmatrix}1 & 0 \\0 & 1 \\j & 0 \\0 & {- j}\end{bmatrix}\quad$ Π · Π · Π · Π · W_(N) _(t) _(×2) ¹² W_(N) _(t) _(×2)¹³ W_(N) _(t) _(×2) ¹⁴ W_(N) _(t) _(×2) ¹⁵ $\begin{bmatrix}1 & 0 \\0 & 1 \\{- j} & 0 \\0 & 1\end{bmatrix}\quad$ $\begin{bmatrix}1 & 0 \\0 & 1 \\{- j} & 0 \\0 & {- 1}\end{bmatrix}\quad$ $\begin{bmatrix}1 & 0 \\0 & 1 \\{- j} & 0 \\0 & j\end{bmatrix}\quad$ $\begin{bmatrix}1 & 0 \\0 & 1 \\{- j} & 0 \\0 & {- j}\end{bmatrix}\quad$

Meanwhile, according to one embodiment of the present invention,proposed is a method of designing a codebook to apply a physical antennapermutation and virtual swapping in addition. Formula 3 shows aprecoding matrix type to which virtual antenna swapping is applied.W _(N) _(t) _(×2) ^(n)·Ξ  [Formula 3]

In Formula 3, Ξ indicates a virtual antenna swapping matrix. And, thisvirtual antenna swapping matrix can be represented as follows.

$\begin{matrix}{\Xi = \begin{bmatrix}0 & 1 \\1 & 0\end{bmatrix}} & \left\lbrack {{Formula}\mspace{14mu} 4} \right\rbrack\end{matrix}$

If the above-described virtual antenna swapping matrix is applied toTable 16/Table 17, Table 18/Table 19 can be generated.

TABLE 18 Number of layers ν Layer-2 codebook (W_(N) _(t) _(×2) · Θ) 2W_(N) _(t) _(×2) ⁰ · W_(N) _(t) _(×2) ¹ · W_(N) _(t) _(×2) ² · W_(N)_(t) _(×2) ³ · Θ Θ Θ Θ $\begin{bmatrix}0 & 1 \\0 & 1 \\1 & 0 \\1 & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 \\0 & 1 \\1 & 0 \\{- 1} & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 \\0 & 1 \\1 & 0 \\j & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 \\0 & 1 \\1 & 0 \\{- j} & 0\end{bmatrix}\quad$ W_(N) _(t) _(×2) ⁴ · W_(N) _(t) _(×2) ⁵ · W_(N) _(t)_(×2) ⁶ · W_(N) _(t) _(×2) ⁷ · Θ Θ Θ Θ $\begin{bmatrix}0 & 1 \\0 & {- 1} \\1 & 0 \\1 & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 \\0 & {- 1} \\1 & 0 \\{- 1} & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 \\0 & {- 1} \\1 & 0 \\j & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 \\0 & {- 1} \\1 & 0 \\{- j} & 0\end{bmatrix}\quad$ W_(N) _(t) _(×2) ⁸ · W_(N) _(t) _(×2) ⁹ · W_(N) _(t)_(×2) ¹⁰ · W_(N) _(t) _(×2) ¹¹ · Θ Θ Θ Θ $\begin{bmatrix}0 & 1 \\0 & j \\1 & 0 \\1 & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 \\0 & j \\1 & 0 \\{- 1} & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 \\0 & j \\1 & 0 \\j & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 \\0 & j \\1 & 0 \\{- j} & 0\end{bmatrix}\quad$ W_(N) _(t) _(×2) ¹² · W_(N) _(t) _(×2) ¹³ · W_(N)_(t) _(×2) ¹⁴ · W_(N) _(t) _(×2) ¹⁵ · Θ Θ Θ Θ $\begin{bmatrix}0 & 1 \\0 & {- j} \\1 & 0 \\1 & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 \\0 & {- j} \\1 & 0 \\{- 1} & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 \\0 & {- j} \\1 & 0 \\j & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 \\0 & {- j} \\1 & 0 \\{- j} & 0\end{bmatrix}\quad$

TABLE 19 Number of layers ν Layer-2 codebook (Π · W_(N) _(t) _(×2) ^(n)· Θ) 2 Π₁ · W_(N) _(t) _(×2) ⁰· Π₁ · Π₁ · W_(N) _(t) _(×2) ² · Π₁ · ΘW_(N) _(×2) ¹ · Θ Θ W_(N) _(t) _(×2) ³ · Θ $\begin{bmatrix}0 & 1 \\1 & 0 \\0 & 1 \\1 & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 \\1 & 0 \\0 & 1 \\{- 1} & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 \\1 & 0 \\0 & 1 \\j & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 \\1 & 0 \\0 & 1 \\{- j} & 0\end{bmatrix}\quad$ Π₁ · W_(N) _(t) _(×2) ⁴ · Π₁ · Π₁ · W_(N) _(t) _(×2)⁶ · Π₁ · Θ W_(N) _(×2) ⁵ · Θ Θ W_(N) _(t) _(×2) ⁷ · Θ $\begin{bmatrix}0 & 1 \\{- 1} & 0 \\0 & 1 \\1 & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 \\{- 1} & 0 \\0 & 1 \\{- 1} & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 \\{- 1} & 0 \\0 & 1 \\j & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 \\{- 1} & 0 \\0 & 1 \\{- j} & 0\end{bmatrix}\quad$ Π₁ · W_(N) _(t) _(×2) ⁸ · Π₁ · Π₁ · W_(N) _(t) _(×2)¹⁰ · Π₁ · Θ W_(N) _(×2) ⁹ · Θ Θ W_(N) _(t) _(×2) ¹¹ · Θ $\begin{bmatrix}0 & 1 \\j & 0 \\0 & 1 \\1 & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 \\j & 0 \\0 & 1 \\{- 1} & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 \\j & 0 \\0 & 1 \\j & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 \\j & 0 \\0 & 1 \\{- j} & 0\end{bmatrix}\quad$ Π₁ · W_(N) _(t) _(×2) ¹² · Π₁ · Π₁ · W_(N) _(t)_(×2) ¹⁴ · Π₁ · Θ W_(N) _(×2) ¹³ · Θ Θ W_(N) _(t) _(×2) ¹⁵ · Θ$\begin{bmatrix}0 & 1 \\{- j} & 0 \\0 & 1 \\1 & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 \\{- j} & 0 \\0 & 1 \\{- 1} & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 \\{- j} & 0 \\0 & 1 \\j & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 \\{- j} & 0 \\0 & 1 \\{- j} & 0\end{bmatrix}\quad$

Meanwhile, according to one embodiment of the present invention,proposed is a rank-2 codebook of a type to which a physical antennapermutation is partially applied. In particular, parts of Table 16 andTable 17 can be included in a combined codebook type. Table 20/Table 21shows a case that one permutation matrix is used per codebook, whiletable 22/Table 23 shows a case that two permutation matrixes are usedper codebook.

TABLE 20 Number of layers ν Layer-2 codebook 2 W_(N) _(t) _(×2) ² _(,)W_(N) _(t) _(×2) ³ _(,) W_(N) _(t) _(×2) ⁶ _(,) W_(N) _(t) _(×2) ⁷ _(,)W_(N) _(t) _(×2) ⁸ _(,) W_(N) _(t) _(×2) ⁹ _(,) W_(N) _(t) _(×2) ¹² _(,)W_(N) _(t) _(×2) ¹³ _(,) Π₁ · W_(N) _(t) _(×2) ⁰ _(,) Π₁ · W_(N) _(t)_(×2) ¹ _(,) Π₁ · W_(N) _(t) _(×2) ⁴ _(,) Π₁ · W_(N) _(t) _(×2) ⁵ _(,)Π_(1 ·) W_(N) _(t) _(×2) ⁶ _(,) Π₁ · W_(N) _(t) _(×2) ⁷ _(,) Π₁ · W_(N)_(t) _(×2) ¹⁰ _(,) Π₁ · W_(N) _(t) _(×2) ¹¹ _(,)

Table 20 is characterized in that a subset of a total combinationcodebook is combined with a subset of a permutated codebook. Allpermutated elements do not originate from the subset of the totalcombination codebook. And, Table 20 shows a case that one permutationmatrix is used only.

TABLE 21 Number of layers ν Layer-2 codebook 2 W_(N) _(t) _(×2) ² _(,)W_(N) _(t) _(×2) ³ _(,) W_(N) _(t) _(×2) ⁶ _(,) W_(N) _(t) _(×2) ⁷ _(,)W_(N) _(t) _(×2) ⁸ _(,) W_(N) _(t) _(×2) ⁹ _(,) W_(N) _(t) _(×2) ¹² _(,)W_(N) _(t) _(×2) ¹³ _(,) Π₁ · W_(N) _(t) _(×2) ² _(,) Π₁ · W_(N) _(t)_(×2) ³ _(,) Π₁ · W_(N) _(t) _(×2) ⁶ _(,) Π₁ · W_(N) _(t) _(×2) ⁷ _(,)Π₁ · W_(N) _(t) _(×2) ⁸ _(,) Π₁ · W_(N) _(t) _(×2) ⁹ _(,) Π₁ · W_(N)_(t) _(×2) ¹² _(,) Π₁ · W_(N) _(t) _(×2) ¹³ _(,)

Table 21 is characterized in that a subset of a total combinationcodebook is combined with a subset of a permutated codebook. Allpermutated elements originate from the subset of the total combinationcodebook. And, Table 21 shows a case that one permutation matrix is usedonly.

TABLE 22 Number of layers ν Layer-2 codebook 2 W_(N) _(t) _(×2) ² _(,)W_(N) _(t) _(×2) ³ _(,) W_(N) _(t) _(×2) ⁶ _(,) W_(N) _(t) _(×2) ⁷ _(,)W_(N) _(t) _(×2) ⁸ _(,) W_(N) _(t) _(×2) ⁹ _(,) W_(N) _(t) _(×2) ¹² _(,)W_(N) _(t) _(×2) ¹³ _(,) Π₁ · W_(N) _(t) _(×2) ⁰ _(,) Π₁ · W_(N) _(t)_(×2) ¹ _(,) Π₁ · W_(N) _(t) _(×2) ⁴ _(,) Π₁ · W_(N) _(t) _(×2) ⁵ _(,)Π₃ · W_(N) _(t) _(×2) ⁸ _(,) Π₃ · W_(N) _(t) _(×2) ⁹ _(,) Π₃ · W_(N)_(t) _(×2) ¹² _(,) Π₃ · W_(N) _(t) _(×2) ¹³ _(,)

Table 22 is characterized in that a subset of a total combinationcodebook is combined with a subset of a permutated codebook. Allpermutated elements do not originate from the subset of the totalcombination codebook. And, Table 22 shows a case that a plurality ofpermutation matrixes is used.

TABLE 23 Number of layers ν Layer-2 codebook 2 W_(N) _(t) _(×2) ² _(,)W_(N) _(t) _(×2) ³ _(,) W_(N) _(t) _(×2) ⁶ _(,) W_(N) _(t) _(×2) ⁷ _(,)W_(N) _(t) _(×2) ⁸ _(,) W_(N) _(t) _(×2) ⁹ _(,) W_(N) _(t) _(×2) ¹² _(,)W_(N) _(t) _(×2) ¹³ _(,) Π₁ · W_(N) _(t) _(×2) ² _(,) Π₁ · W_(N) _(t)_(×2) ³ _(,) Π₁ · W_(N) _(t) _(×2) ⁶ _(,) Π₁ · W_(N) _(t) _(×2) ⁷ _(,)Π₃ · W_(N) _(t) _(×2) ⁸ _(,) Π₃ · W_(N) _(t) _(×2) ⁹ _(,) Π₃ · W_(N)_(t) _(×2) ¹² _(,) Π₃ · W_(N) _(t) _(×2) ¹³ _(,)

Table 23 is characterized in that a subset of a total combinationcodebook is combined with a subset of a permutated codebook. Allpermutated elements originate from the subset of the total combinationcodebook. And, Table 22 shows a case that a plurality of permutationmatrixes is used.

Meanwhile, according to another embodiment of the present invention,proposed is a codebook of a type in which permutation and swapping arecombined with each other. Examples of a rank-2 codebook according to thepresent embodiment are shown as follows.

TABLE 24 Number of layers ν Layer-2 codebook 2 W_(N) _(t) _(×2) ² _(,)W_(N) _(t) _(×2) ³ _(,) W_(N) _(t) _(×2) ⁶ _(,) W_(N) _(t) _(×2) ⁷ _(,)W_(N) _(t) _(×2) ⁸ _(,) W_(N) _(t) _(×2) ⁹ _(,) W_(N) _(t) _(×2) ¹² _(,)W_(N) _(t) _(×2) ¹³ _(,) Π₁ · W_(N) _(t) _(×2) ⁰ _(,) · Ξ_(,) Π₁ · W_(N)_(t) _(×2) ¹ _(,) · Ξ_(,) Π₁ · W_(N) _(t) _(×2) ⁴ _(,) · Ξ_(,) Π₁ ·W_(N) _(t) _(×2) ⁵ _(,) · Ξ_(,) Π₁ · W_(N) _(t) _(×2) ⁶ _(,) · Ξ_(,) Π₁· W_(N) _(t) _(×2) ⁷ _(,) · Ξ_(,) Π₁ · W_(N) _(t) _(×2) ¹⁰ _(,) · Ξ_(,)Π₁ · W_(N) _(t) _(×2) ¹¹ _(,) · Ξ_(,)

TABLE 25 Number of layers ν Layer-2 codebook 2 W_(N) _(t) _(×2) ² _(,)W_(N) _(t) _(×2) ³ _(,) W_(N) _(t) _(×2) ⁶ _(,) W_(N) _(t) _(×2) ⁷ _(,)W_(N) _(t) _(×2) ⁸ _(,) W_(N) _(t) _(×2) ⁹ _(,) W_(N) _(t) _(×2) ¹² _(,)W_(N) _(t) _(×2) ¹³ _(,) Π₁ · W_(N) _(t) _(×2) ² _(,) · Ξ_(,) Π₁ · W_(N)_(t) _(×2) ³ · Ξ_(,) Π₁ · W_(N) _(t) _(×2) ² · Ξ_(,) Π₁ · W_(N) _(t)_(×2) ⁷ · Ξ_(,) Π₁ · W_(N) _(t) _(×2) ⁶ · Ξ_(,) Π₁ · W_(N) _(t) _(×2) ⁹· Ξ_(,) Π₁ · W_(N) _(t) _(×2) ¹² · Ξ_(,) Π₁ · W_(N) _(t) _(×2) ¹³ ·Ξ_(,)

Besides, various combinations are possible as follows.

TABLE 26 Number of layers ν Layer-2 codebook 2 W_(N) _(t) _(×2) ² _(,)W_(N) _(t) _(×2) ³ _(,) W_(N) _(t) _(×2) ⁶ _(,) W_(N) _(t) _(×2) ⁷ _(,)W_(N) _(t) _(×2) ⁸ _(,) W_(N) _(t) _(×2) ⁹ _(,) W_(N) _(t) _(×2) ¹² _(,)W_(N) _(t) _(×2) ¹³ _(,) Π · W_(N) _(t) _(×2) ⁰ _(,) Π · W_(N) _(t)_(×2) ¹ _(,) Π · W_(N) _(t) _(×2) ⁴ _(,) Π · W_(N) _(t) _(×2) ⁵ _(,)W_(N) _(t) _(×2) ⁶ · Ξ_(,) W_(N) _(t) _(×2) ⁷ · Ξ_(,) W_(N) _(t) _(×2)¹⁰ · Ξ_(,) W_(N) _(t) _(×2) ¹¹ · Ξ_(,)

TABLE 27 Number of layers ν Layer-2 codebook 2 W_(N) _(t) _(×2) ² _(,)W_(N) _(t) _(×2) ³ _(,) W_(N) _(t) _(×2) ⁶ _(,) W_(N) _(t) _(×2) ⁷ _(,)W_(N) _(t) _(×2) ⁸ _(,) W_(N) _(t) _(×2) ⁹ _(,) W_(N) _(t) _(×2) ¹² _(,)W_(N) _(t) _(×2) ¹³ _(,) Π · W_(N) _(t) _(×2) ⁰ _(,) Π · W_(N) _(t)_(×2) ¹ _(,) Π · W_(N) _(t) _(×2) ⁴ _(,) Π · W_(N) _(t) _(×2) ⁵ _(,)W_(N) _(t) _(×2) ⁶ · Ξ_(,) W_(N) _(t) _(×2) ⁷ · Ξ_(,) W_(N) _(t) _(×2)¹⁰ · Ξ_(,) W_(N) _(t) _(×2) ¹¹ · Ξ_(,)

TABLE 28 Number of layers ν Layer-2 codebook 2 W_(N) _(t) _(×2) ² _(,)W_(N) _(t) _(×2) ³ _(,) W_(N) _(t) _(×2) ⁶ _(,) W_(N) _(t) _(×2) ⁷ _(,)W_(N) _(t) _(×2) ⁸ _(,) W_(N) _(t) _(×2) ⁹ _(,) W_(N) _(t) _(×2) ¹² _(,)W_(N) _(t) _(×2) ¹³ _(,) Π · W_(N) _(t) _(×2) ⁰ _(,) Π · W_(N) _(t)_(×2) ¹ _(,) Π · W_(N) _(t) _(×2) ⁴ _(,) Π · W_(N) _(t) _(×2) ⁵ · Ξ_(,)Π · W_(N) _(t) _(×2) ⁶ · Ξ_(,) Π · W_(N) _(t) _(×2) ⁷ · Ξ_(,) W_(N) _(t)_(×2) ¹⁰ · Ξ_(,) W_(N) _(t) _(×2) ¹¹ · Ξ_(,)

TABLE 29 Number of layers ν Layer-2 codebook 2 W_(N) _(t) _(×2) ² _(,)W_(N) _(t) _(×2) ³ _(,) W_(N) _(t) _(×2) ⁶ _(,) W_(N) _(t) _(×2) ⁷ _(,)W_(N) _(t) _(×2) ⁸ _(,) W_(N) _(t) _(×2) ⁹ _(,) W_(N) _(t) _(×2) ¹² _(,)W_(N) _(t) _(×2) ¹³ _(,) Π · W_(N) _(t) _(×2) ² _(,) Π · W_(N) _(t)_(×2) ³ _(,) Π · W_(N) _(t) _(×2) ⁶ _(,) Π₁ · W_(N) _(t) _(×2) ⁷ · Ξ_(,)Π₁ · W_(N) _(t) _(×2) ⁸ · Ξ_(,) Π₁ · W_(N) _(t) _(×2) ⁹ · Ξ_(,) W_(N)_(t) _(×2) ¹² · Ξ_(,) W_(N) _(t) _(×2) ¹³ · Ξ_(,)

According to another embodiment of the present invention, an antennagroup selection matrix is configured as Table 30 or can be configured bybeing combined with other precoding matrixes as Tables 31 to 33.

TABLE 30 Number of layers ν Layer-2 codebook (W_(N) _(t) _(×2) ^(n)) 2$\begin{bmatrix}{\overset{\_}{v}}_{1} & {\overset{\_}{v}}_{2} \\\overset{\_}{z} & \overset{\_}{z}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{3} & {\overset{\_}{v}}_{4} \\\overset{\_}{z} & \overset{\_}{z}\end{bmatrix},\begin{bmatrix}\overset{\_}{z} & \overset{\_}{z} \\{\overset{\_}{v}}_{1} & {\overset{\_}{v}}_{2}\end{bmatrix},\begin{bmatrix}\overset{\_}{z} & \overset{\_}{z} \\{\overset{\_}{v}}_{3} & {\overset{\_}{v}}_{4}\end{bmatrix}$ ${\Pi \cdot \begin{bmatrix}{\overset{\_}{v}}_{1} & {\overset{\_}{v}}_{2} \\\overset{\_}{z} & \overset{\_}{z}\end{bmatrix}},{\Pi \cdot \begin{bmatrix}{\overset{\_}{v}}_{3} & {\overset{\_}{v}}_{4} \\\overset{\_}{z} & \overset{\_}{z}\end{bmatrix}},{\Pi \cdot \begin{bmatrix}\overset{\_}{z} & \overset{\_}{z} \\{\overset{\_}{v}}_{1} & {\overset{\_}{v}}_{2}\end{bmatrix}},{\Pi \cdot \begin{bmatrix}\overset{\_}{z} & \overset{\_}{z} \\{\overset{\_}{v}}_{3} & {\overset{\_}{v}}_{4}\end{bmatrix}}$

TABLE 31 Number of layers ν Layer-2 codebook (W_(N) _(t) _(×2) ^(n)) 2$\begin{bmatrix}{\overset{\_}{v}}_{1} & {\overset{\_}{v}}_{2} \\\overset{\_}{z} & \overset{\_}{z}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{3} & {\overset{\_}{v}}_{4} \\\overset{\_}{z} & \overset{\_}{z}\end{bmatrix},\begin{bmatrix}\overset{\_}{z} & \overset{\_}{z} \\{\overset{\_}{v}}_{1} & {\overset{\_}{v}}_{2}\end{bmatrix},\begin{bmatrix}\overset{\_}{z} & \overset{\_}{z} \\{\overset{\_}{v}}_{3} & {\overset{\_}{v}}_{4}\end{bmatrix}$ W_(N) _(t) _(×2) ², W_(N) _(t) _(×2) ³, W_(N) _(t) _(×2)⁶, W_(N) _(t) _(×2) ⁷, W_(N) _(t) _(×2) ⁸, W_(N) _(t) _(×2) ⁹, W_(N)_(t) _(×2) ¹², W_(N) _(t) _(×2) ¹³, Π₁ · W_(N) _(t) _(×2) ², Π₁ · W_(N)_(t) _(×2) ³, Π₁ · W_(N) _(t) _(×2) ⁶, Π₁ · W_(N) _(t) _(×2) ⁷, Π₁ ·W_(N) _(t) _(×2) ⁸, Π₁ · W_(N) _(t) _(×2) ⁹, Π₁ · W_(N) _(t) _(×2) ¹²,Π₁ · W_(N) _(t) _(×2) ¹³,

TABLE 32 Number of layers ν Layer-2 codebook (W_(N) _(t) _(×2) ^(n)) 2$\begin{bmatrix}{\overset{\_}{v}}_{1} & {\overset{\_}{v}}_{2} \\\overset{\_}{z} & \overset{\_}{z}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{3} & {\overset{\_}{v}}_{4} \\\overset{\_}{z} & \overset{\_}{z}\end{bmatrix},\begin{bmatrix}\overset{\_}{z} & \overset{\_}{z} \\{\overset{\_}{v}}_{1} & {\overset{\_}{v}}_{2}\end{bmatrix},\begin{bmatrix}\overset{\_}{z} & \overset{\_}{z} \\{\overset{\_}{v}}_{3} & {\overset{\_}{v}}_{4}\end{bmatrix}$ W_(N) _(t) _(×2) ², W_(N) _(t) _(×2) ³, W_(N) _(t) _(×2)⁶, W_(N) _(t) _(×2) ⁷, Π · W_(N) _(t) _(×2) ⁰, Π · W_(N) _(t) _(×2) ¹, Π· W_(N) _(t) _(×2) ⁴, Π · W_(N) _(t) _(×2) ⁵, Π · W_(N) _(t) _(×2) ⁶, Π· W_(N) _(t) _(×2) ⁷, Π · W_(N) _(t) _(×2) ¹⁰, Π · W_(N) _(t) _(×2) ¹¹,

TABLE 33 Number of layers ν Layer-2 codebook (W_(N) _(t) _(×2) ^(n)) 2$\begin{bmatrix}{\overset{\_}{v}}_{1} & {\overset{\_}{v}}_{2} \\\overset{\_}{z} & \overset{\_}{z}\end{bmatrix},\begin{bmatrix}{\overset{\_}{v}}_{3} & {\overset{\_}{v}}_{4} \\\overset{\_}{z} & \overset{\_}{z}\end{bmatrix},\begin{bmatrix}\overset{\_}{z} & \overset{\_}{z} \\{\overset{\_}{v}}_{1} & {\overset{\_}{v}}_{2}\end{bmatrix},\begin{bmatrix}\overset{\_}{z} & \overset{\_}{z} \\{\overset{\_}{v}}_{3} & {\overset{\_}{v}}_{4}\end{bmatrix}$ ${\Pi \cdot \begin{bmatrix}{\overset{\_}{v}}_{1} & {\overset{\_}{v}}_{2} \\\overset{\_}{z} & \overset{\_}{z}\end{bmatrix}},{\Pi \cdot \begin{bmatrix}{\overset{\_}{v}}_{3} & {\overset{\_}{v}}_{4} \\\overset{\_}{z} & \overset{\_}{z}\end{bmatrix}},{\Pi \cdot \begin{bmatrix}\overset{\_}{z} & \overset{\_}{z} \\{\overset{\_}{v}}_{1} & {\overset{\_}{v}}_{2}\end{bmatrix}},{\Pi \cdot \begin{bmatrix}\overset{\_}{z} & \overset{\_}{z} \\{\overset{\_}{v}}_{3} & {\overset{\_}{v}}_{4}\end{bmatrix}}$ W_(N) _(t) _(×2) ², W_(N) _(t) _(×2) ³, W_(N) _(t) _(×2)⁶, W_(N) _(t) _(×2) ⁷, Π · W_(N) _(t) _(×) ⁰, Π · W_(N) _(t) _(×) ¹, Π ·W_(N) _(t) _(×) ⁴, Π · W_(N) _(t) _(×) ⁵, Π · W_(N) _(t) _(×) ⁶, Π ·W_(N) _(t) _(×) ⁷, Π · W_(N) _(t) _(×) ¹⁰, Π · W_(N) _(t) _(×) ¹¹,

Rank-3 Codebook

According to one embodiment of the present invention, 4Tx rank-3codebook design is approached in two viewpoints.

(1) Viewpoint of Antenna Power Balance

A most feasible type of 4Tx rank-3 codebook is explained as follows.First of all, the zero vector/matrix shown in Table 3 is usable forantenna group separation.

$\begin{matrix}{W_{N_{t} \times 3}^{n} \in {\begin{bmatrix}{\overset{\_}{v}}_{i} & \overset{\_}{z} & {\overset{\_}{v}}_{k} \\\overset{\_}{z} & {\overset{\_}{v}}_{j} & \overset{\_}{z}\end{bmatrix}\mspace{14mu}{{or}\mspace{14mu}\begin{bmatrix}{\overset{\_}{v}}_{i} & \overset{\_}{z} & \overset{\_}{z} \\\overset{\_}{z} & {\overset{\_}{v}}_{j} & {\overset{\_}{v}}_{k}\end{bmatrix}}}} & \left\lbrack {{Formula}\mspace{14mu} 5} \right\rbrack\end{matrix}$

It is able to consider a matrix type that is normalized by multiplyingthe precoding matrix type of Formula 5 by a same scaling coefficient. Inthis case, i, j, k can include independent numbers, respectively.Physical antenna permutation (e.g., Π·W_(N) _(t) _(×3) ^(n)), virtualantenna permutation (e.g., W_(N) _(t) _(×3) ^(n)·Θ), and totalpermutation (e.g., Π·W_(N) _(t) _(×3) ^(n)·Θ) can be applied to therank-3 codebook in the same manner of the rank-2 codebook. And, virtualantenna permutation Θ can be prescribed as follows.

TABLE 34 Θ Θ₁ Θ₂ Θ₃ $\begin{bmatrix}1 & 0 & 0 \\0 & 0 & 1 \\0 & 1 & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 & 0 \\1 & 0 & 0 \\0 & 0 & 1\end{bmatrix}\quad$ $\begin{bmatrix}0 & 1 & 0 \\0 & 0 & 1 \\1 & 0 & 0\end{bmatrix}\quad$ Θ₄ Θ₅ $\begin{bmatrix}0 & 0 & 1 \\1 & 0 & 0 \\0 & 1 & 0\end{bmatrix}\quad$ $\begin{bmatrix}0 & 0 & 1 \\0 & 1 & 0 \\1 & 0 & 0\end{bmatrix}\quad$

Yet, one preferred embodiment of the present invention proposes that aprecoding matrix of a following type, which enables perfect powerbalance per antenna, is included in a rank-3 codebook.

$\begin{matrix}{W_{N_{t} \times 3}^{n} = \begin{bmatrix}{\overset{\_}{v}}_{i} & \overset{\_}{z} & {\overset{\_}{v}}_{k} \\\overset{\_}{z} & {\overset{\_}{v}}_{j} & v_{l}\end{bmatrix}} & \left\lbrack {{Formula}\mspace{14mu} 6} \right\rbrack\end{matrix}$

In Formula 6, i, j and k can be arbitrary independent indexes in Table 2or Table 3, respectively. According to one embodiment of the presentinvention, if a normalization coefficient for ν _(i) and ν _(j) is setto 1/√{square root over (α)} and a normalization coefficient for ν _(k)and the ν _(l) is set to 1/√{square root over (β)}, the two coefficientscan differ from each other. For instance, if α=2β, it is able tosimultaneously match power balance per layer and power balance perantenna both.

If it is set to α=β, it becomes a precoding matrix of a type thatmatches the power balance per antenna only. In this case, Formula 6 canbe represented as follows.

$\begin{matrix}{W_{N_{t} \times 3}^{n} = {\frac{1}{\sqrt{\delta}}\begin{bmatrix}{\overset{\_}{v}}_{i} & \overset{\_}{z} & {\overset{\_}{v}}_{k} \\\overset{\_}{z} & {\overset{\_}{v}}_{j} & {\overset{\_}{v}}_{l}\end{bmatrix}}} & \left\lbrack {{Formula}\mspace{14mu} 7} \right\rbrack\end{matrix}$

According to the present embodiment, physical antenna permutation (e.g.,Π·W_(N) _(t) _(×3) ^(n)), virtual antenna permutation (e.g., W_(N) _(t)_(×3) ^(n)·Θ), and total permutation (e.g., Π·W_(N) _(t) _(×3) ^(n)·Θ)can be applied in the same manner of the rank-2 codebook. And, virtualantenna permutation Θ can be prescribed as Table 34.

In the precoding matrix type represented by Formula 6 or Formula 7, ν_(i) and ν _(k) are preferably orthogonal to each other. And, ν _(j) andν _(l) are preferably orthogonal to each other as well.

An example for a rank-3 precoding matrix, which meets theabove-mentioned conditions, can be represented as follows.

$\begin{matrix}{{W_{N_{t} \times 3}^{n} = {\begin{bmatrix}1 & 0 & 1 \\{\mathbb{e}}^{{j\theta}_{1}} & 0 & {- {\mathbb{e}}^{{j\theta}_{1}}} \\0 & 1 & 1 \\0 & {\mathbb{e}}^{{j\theta}_{2}} & {- {\mathbb{e}}^{{j\theta}_{2}}}\end{bmatrix}\mspace{14mu}{or}}}{W_{N_{t} \times 3}^{n} = \begin{bmatrix}1 & 0 & 1 \\{- {\mathbb{e}}^{{j\theta}_{1}}} & 0 & {\mathbb{e}}^{{j\theta}_{1}} \\0 & {\mathbb{e}}^{{j\theta}_{2}} & {\mathbb{e}}^{{j\theta}_{2}} \\0 & {- {\mathbb{e}}^{{j\theta}_{3}}} & {\mathbb{e}}^{{j\theta}_{3}}\end{bmatrix}}} & \left\lbrack {{Formula}\mspace{14mu} 8} \right\rbrack\end{matrix}$

Of course, a rank-3 codebook includes a type generated from multiplyingthe type of Formula 8 by a normalization coefficient. In this case,N_(t) is 4, θ₁, θ₂ meets the condition of

${\theta_{2} \in \left\{ {{\frac{2\pi}{N}i},{i = 0},\ldots\mspace{14mu},{N - 1}} \right\}},,$and N is 4 or 8.

Moreover, it is able to consider a type generated from multiplyingFormula 8 by one of various permutations. Theses types can berepresented as follows.

$\begin{matrix}{{{\prod{\cdot W_{N_{t} \times 3}^{n}}} = {\prod{{\cdot \begin{bmatrix}1 & 0 & 1 \\{\mathbb{e}}^{{j\theta}_{1}} & 0 & {- {\mathbb{e}}^{{j\theta}_{1}}} \\0 & 1 & 1 \\0 & {\mathbb{e}}^{{j\theta}_{2}} & {- {\mathbb{e}}^{{j\theta}_{2}}}\end{bmatrix}}\mspace{14mu}{or}}}}{\prod{\cdot \begin{bmatrix}1 & 0 & 1 \\{- {\mathbb{e}}^{{j\theta}_{1}}} & 0 & {\mathbb{e}}^{{j\theta}_{1}} \\0 & {\mathbb{e}}^{{j\theta}_{2}} & {\mathbb{e}}^{{j\theta}_{2}} \\0 & {- {\mathbb{e}}^{{j\theta}_{3}}} & {\mathbb{e}}^{{j\theta}_{3}}\end{bmatrix}}}} & \left\lbrack {{Formula}\mspace{14mu} 9} \right\rbrack \\{{{\prod{\cdot W_{N_{t} \times 3}^{n} \cdot \Theta}} = {\prod{\cdot \begin{bmatrix}1 & 0 & 1 \\{\mathbb{e}}^{{j\theta}_{1}} & 0 & {- {\mathbb{e}}^{{j\theta}_{1}}} \\0 & 1 & 1 \\0 & {\mathbb{e}}^{{j\theta}_{2}} & {- {\mathbb{e}}^{{j\theta}_{2}}}\end{bmatrix} \cdot \Theta}}}\begin{matrix}{{W_{N_{t} \times 3}^{n} \cdot \Theta} = {\begin{bmatrix}1 & 0 & 1 \\{\mathbb{e}}^{{j\theta}_{1}} & 0 & {- {\mathbb{e}}^{{j\theta}_{1}}} \\0 & 1 & 1 \\0 & {\mathbb{e}}^{{j\theta}_{2}} & {- {\mathbb{e}}^{{j\theta}_{2}}}\end{bmatrix} \cdot \Theta}} \\{= {\prod{\cdot \begin{bmatrix}1 & 0 & 1 \\{- {\mathbb{e}}^{{j\theta}_{1}}} & 0 & {\mathbb{e}}^{{j\theta}_{1}} \\0 & {\mathbb{e}}^{{j\theta}_{2}} & {\mathbb{e}}^{{j\theta}_{2}} \\0 & {- {\mathbb{e}}^{{j\theta}_{3}}} & {\mathbb{e}}^{{j\theta}_{3}}\end{bmatrix} \cdot \Theta}}}\end{matrix}} & \left\lbrack {{Formula}\mspace{14mu} 10} \right\rbrack \\{{W_{N_{t} \times 3}^{n} \cdot \Theta} = {\begin{bmatrix}1 & 0 & 1 \\{- {\mathbb{e}}^{{j\theta}_{1}}} & 0 & {\mathbb{e}}^{{j\theta}_{1}} \\0 & {\mathbb{e}}^{{j\theta}_{2}} & {\mathbb{e}}^{{j\theta}_{2}} \\0 & {- {\mathbb{e}}^{{j\theta}_{3}}} & {\mathbb{e}}^{{j\theta}_{3}}\end{bmatrix} \cdot \Theta}} & \;\end{matrix}$

(2) CM Property Maintaining Viewpoint

If MIMO is applied to uplink signal transmission, it may cause such aproblem that a power amplifier of high performance raises a cost of auser equipment. And, PAPR/CM property of the uplink signal transmissionis more important than that of downlink signal transmission. Therefore,a codebook structure for maintaining a good PAPR/CM property needs to betaken into consideration.

PAPR (peak power to average power ratio) is a parameter that indicates aproperty of waveform. This value results from dividing a peak amplitudeof waveform by a time-averaged RMS (root mean square) value of thewaveform and is a dimensionless value. Normally, a PAPR of a singlecarrier signal is better than that of a multi-carrier signal.

In LTE-Advanced, it is able to implement MIMO (multiple input multipleoutput) using SC-FDMA (single carrier-frequency division multipleaccess) to maintain a good CM property. If general precoding is used, asignal carrying information corresponding to several layers ismultiplexed and transmitted via a single antenna, the signal transmittedvia this antenna can be regarded as a sort of multi-carrier signal. PAPRis associated with a dynamic range a power amplifier in a transmittingside should support. And, a CM (cubic metric) value is another numericalvalue indicating a numerical value represented by the PAPR.

In order to maintain the above-mentioned good PAPR/CM property for theuplink signal transmission, a combined type of SC-FDMA and MIMO ispreferably taken into consideration.

FIG. 3 is a diagram for explaining general SC-FDMA.

Referring to FIG. 3, in both OFDM and SC-FDMA schemes, a serial signalis converted to a parallel signal, the parallel signal is mapped by asubcarrier, IDFT or IFFT is performed thereon, the signal is convertedto a serial signal again, a CP is attached to the serial signal, and thecorresponding signal is then transmitted via an RF module. Yet, theSC-FDMA scheme is characterized in reducing influence of IDFT or IFFTprocessing through DFP spreading after conversion to a serial signalfrom a parallel signal and maintaining a single signal property over apredetermined level.

When MIMO is applied to this SC-FDMA signal transmission, a processorconfiguration of a user equipment is explained as follows.

FIG. 4 is a diagram for detailed configuration of a processor of a userequipment according to one embodiment of the present invention.

Referring to FIG. 4, a processor of a user equipment according to oneembodiment of the present invention includes a layer mapper 1401 mappingan uplink signal by layers of which number corresponding to a specificrank, a prescribed number of DFT modules 1402 performing DFT (discreteFourier transform) spreading on a prescribed number of layer signals,and a precoder 1403 performing precoding on a transmission signal byselecting a precoding matrix from a codebook stored in a memory 22. TheDFT module 1402 for transmitting an uplink signal by SC-FDMA, as shownin FIG. 4, is arranged in front of the precoder 1403 and in rear of thelayer mapper 1401. The DFT-spread signal per layer passes through theprecoding and is then transmitted by being IFFT inverse-spread.Therefore, it is able to maintain a good PAPR/CM property due to thecancellation effect between DFT spreading and IFFT inverse spreading.

According to one embodiment of the present invention, proposed is amethod of designing a rank-3 codebook to maintain an optimal PAPR/CMproperty in a manner that each row of a precoding matrix is made toinclude one component except 0 only. In case of using such a precodingmatrix including one component except 0 in each row, a plurality of datasymbols are not combined with each antenna port. Therefore, it is ableto maintain a good CM property. Moreover, as mentioned in the foregoingdescription with reference to FIG. 4, if one layer signal is set to betransmitted via one antenna in performing precoding after DFT spreading,it is able to directly cancel the effect of IFFT inverse spreading byDFT spreading.

A precoding matrix of a rank-3 codebook according to the presentembodiment can be represented as follows.

$\begin{matrix}{W_{N_{t} \times 3}^{n} = \begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1 \\0 & 0 & {\mathbb{e}}^{j\theta}\end{bmatrix}} & \left\lbrack {{Formula}\mspace{14mu} 11} \right\rbrack\end{matrix}$

Of course, the rank-3 codebook can include a type that the above typerepresented by Formula 11 is multiplied by a normalization coefficient.In Formula 11, N_(t) is 4, θ meets the condition of

${{\;_{\backprime}\theta \in \left\{ {{\frac{2\pi}{N}i},{i = 0},\ldots\mspace{14mu},{N - 1}} \right\}};},$and N is 4 or 8.

A precoding matrix according to the present embodiment can have variouspermutation types as follows.

$\begin{matrix}{{\prod{\cdot W_{N_{t} \times 3}^{n}}} = {\prod{\cdot \begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1 \\0 & 0 & {\mathbb{e}}^{j\theta}\end{bmatrix}}}} & \left\lbrack {{Formula}\mspace{14mu} 12} \right\rbrack \\{{{\prod{\cdot W_{N_{t} \times 3}^{n} \cdot \Theta}} = {\prod{{\cdot \begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1 \\0 & 0 & {\mathbb{e}}^{j\theta}\end{bmatrix} \cdot \Theta}\mspace{14mu}{or}}}}{{W_{N_{t} \times 3}^{n} \cdot \Theta} = {\begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1 \\0 & 0 & {\mathbb{e}}^{j\theta}\end{bmatrix} \cdot \Theta}}} & \left\lbrack {{Formula}\mspace{14mu} 13} \right\rbrack\end{matrix}$

In case of the precoding matrixes represented as Formulas 11 to 13,either antenna power balancing or layer power balancing can beperformed. And, it is unable to simultaneously perform both of theantenna power balancing and the layer power balancing.

In viewpoint of CM property, the precoding matrixes shown in Formulas 7to 10 can be regarded as matrixes for maintaining a good CM property inapart. Regarding the precoding matrixes shown in Formulas 7 to 10, twonon-zero components are included in each row. Comparing the precodingmatrixes shown in Formulas 7 to 10 to a precoding matrix, in which everycomponent has a constant modulus, since two symbols are combined perantenna, it can be regarded as maintaining a good CM property.

Meanwhile, according to one preferred embodiment of the presentinvention for 4Tx rank-3 codebook, proposed is a combined type codebook,which includes a precoding matrix of an antenna power balance consideredtype as a first type precoding matrix and a precoding matrix of a typeincluding one non-zero component in one row as a second type precodingmatrix, for using both of the first and second type precoding matrixes.

It is understood that the above-mentioned embodiments of the rank-1,rank-2 and rank-3 of the 4Tx antenna codebook are usable by beingcombined into a type including a prescribed number of precoding matrixesper rank in one codebook.

In the following description, a base station and a user equipment, whichuse the above described codebook, are explained.

FIG. 5 is a diagram for configurations of a base station and a userequipment.

Referring to FIG. 5, a base station 10 can include a processor 11, amemory 12 and an RF module 13 as a transceiving module for performing areception of an uplink signal and a transmission of a downlink signal.The processor 11 of the base station 10 controls the downlink signaltransmission using information, which is stored in the memory 12 for thedownlink signal transmission, e.g., a specific precoding matrix within acodebook for the downlink signal transmission. And, the processor 11 ofthe base station 10 is able to control the downlink signal receptionusing information stored in the memory 12 for the uplink signalreception. For instance, the processor 11 is able to control a signalreceiving process for multiplying an uplink signal by Hermitian matrixof the same precoding matrix used by a user equipment 20 as a reverseprocess of precoding. The memory 12 of the base station 10 according tothe present embodiment is proposed to store the above-mentioned codebookas an uplink 4Tx codebook. Moreover, a functionality module forperforming a precoding relevant function of the processor 11 can beseparately configured with a precoder (not shown in the drawing).

The user equipment 20 can include a processor 21, a memory 22 and an RFmodule 23 as a transceiving module for performing a transmission of anuplink signal and a reception of a downlink signal. The processor 21controls the uplink signal transmission using information, which isstored in the memory 22 for the uplink signal transmission, e.g., aspecific precoding matrix within a codebook for the uplink signaltransmission, as mentioned in the foregoing description of theembodiment for the uplink signal transmission. And, the processor 21 isable to control the downlink signal reception using information storedin the memory 22 for the downlink signal reception. For instance, theprocessor 21 is able to control a signal receiving process formultiplying an uplink signal by Hermitian matrix of the same precodingmatrix used by the base station 10 as a reverse process of precoding.The memory 22 of the user equipment 20 according to the presentembodiment is proposed to store the above-mentioned codebook as anuplink 4Tx codebook. Moreover, the detailed configuration of theprocessor 21 can have the former configuration described with referenceto FIG. 4.

While the present invention has been described and illustrated hereinwith reference to the preferred embodiments thereof, it will be apparentto those skilled in the art that various modifications and variationscan be made therein without departing from the spirit and scope of theinvention. Thus, it is intended that the present invention covers themodifications and variations of this invention that come within thescope of the appended claims and their equivalents. And, it isapparently understandable that an embodiment is configured by combiningclaims failing to have relation of explicit citation in the appendedclaims together or can be included as new claims by amendment afterfiling an application.

Accordingly, the above description is mainly made with reference to acase of a follow-up model of 3GPP LTE system, e.g., a case of 3GPP LTE-Asystem. And, the present invention is a next generation mobilecommunication technology and is applicable to IEEE series or systemsaccording to other standards by the same principle.

What is claimed is:
 1. A method of transmitting a signal, which istransmitted to a base station by a user equipment configured to use 4antennas, the method comprising: obtaining transmission rankinformation; outputting a precoded signal by precoding a number of layersignals, the number corresponding to a transmission rank included in thetransmission rank information, using a specific precoding matrixcorresponding to the transmission rank, wherein the specific precodingmatrix is selected from a 4-antenna codebook; and transmitting theprecoded signal to the base station, wherein the 4 antennas are groupedinto a first antenna group including two of the 4 antennas and a secondantenna group including the other two of the 4 antennas, and wherein the4-antenna codebook includes a first type precoding matrix, in which twocomponents corresponding to one of the first and second antenna groupsare zero and two components corresponding to the other one of the firstand second antenna groups construct a discrete Fourier transform (DFT)matrix, and a second type precoding matrix, in which two componentscorresponding to the first antenna group and two componentscorresponding to the second antenna group construct DFT matrixes for arank of
 1. 2. The method of claim 1, wherein the first type precodingmatrix is an antenna group selection matrix and wherein the second typeprecoding matrix is a DFT matrix.
 3. The method of claim 1, wherein thesecond type precoding matrix includes a code in which the two componentscorresponding to the first antenna group and the two componentscorresponding to the second antenna group are mutually orthogonal. 4.The method of claim 1, wherein the 4-antenna codebook further includes aprecoding matrix, in which two components corresponding to either thefirst antenna group or the second antenna group are 0 in a first columnand two components corresponding to either the second antenna group orthe first antenna group are 0 in a second column, for a rank of
 2. 5.The method of claim 4, wherein the 4-antenna codebook further includesat least one selected from the group consisting of a precoding matrixfor performing a layer swapping function of changing positions of twolayer signals and an antenna permutation precoding matrix for changing aposition of an antenna, for the rank of
 2. 6. The method of claim 1,wherein each of the first type precoding matrix and the second typeprecoding matrix is a precoding matrix multiplied by a same constant. 7.The method of claim 6, wherein the first type precoding matrix isconfigured to transmit the precoded signal to the base station using ½of a maximum available transmission power of the user equipment.
 8. Amethod of transmitting a signal, which is transmitted to a base stationby a user equipment configured to use 4 antennas grouped into a firstantenna group including two of the 4 antennas and a second antenna groupincluding the other two of the 4 antennas, the method comprising:turning off the first antenna group in a specific situation; andtransmitting the signal to the base station via the second antennagroup, wherein turning off the first antenna group is performed byprecoding using a rank-1 precoding matrix, and wherein the rank-1precoding matrix includes a precoding matrix, in which two componentscorresponding to the first antenna group are zero and two componentscorresponding to the second antenna group construct a discrete Fouriertransform (DFT) matrix.
 9. A method of receiving a signal, which isreceived by a base station from a user equipment configured to use 4antennas, the method comprising: receiving a reception signal from theuser equipment; obtaining a transmission rank and precoding matrixidentification information used by the user equipment for the receptionsignal; and performing reverse processing of precoding on the receptionsignal using a specific precoding matrix corresponding to thetransmission rank and precoding matrix identification informationselected from a 4-antenna codebook, wherein the 4 antennas are groupedinto a first antenna group including two of the 4 antennas and a secondantenna group including the other two of the 4 antennas, and wherein the4-antenna codebook includes a first type precoding matrix, in which twocomponents corresponding to one of the first and second antenna groupsare zero and two components corresponding to the other one of the firstand second antenna groups construct a discrete Fourier transform (DFT)matrix, and a second type precoding matrix, in which two componentscorresponding to the first antenna group and two componentscorresponding to the second antenna group construct DFT matrixes for arank of
 1. 10. The method of claim 9, wherein the first type precodingmatrix is an antenna group selection matrix and the second typeprecoding matrix is a DFT matrix.
 11. The method of claim 9, wherein the4-antenna codebook further includes a precoding matrix, in which twocomponents corresponding to either the first antenna group or the secondantenna group are 0 in a first column and two components correspondingto either the second antenna group or the first antenna group are 0 in asecond column, for a rank of
 2. 12. A user equipment in a wirelesscommunication system, comprising: a first antenna group including afirst antenna and a second antenna; a second antenna group including athird antenna and a fourth antenna; a memory configured to store a4-antenna codebook including a first type precoding matrix, in which twocomponents corresponding to one of the first and second antenna groupsare zero and two components corresponding to the other one of the firstand second antenna groups construct a discrete Fourier transform (DFT)matrix, and a second type precoding matrix, in which two componentscorresponding to the first antenna group and two componentscorresponding to the second antenna group construct DFT matrixes for arank of 1; and a precoder outputting a precoded signal by precoding anumber of layer signals, the number corresponding to a transmissionrank, using a specific precoding matrix corresponding to thetransmission rank, wherein the specific precoding matrix is selectedfrom the 4-antenna codebook stored in the memory, wherein the precodedsignal is transmitted to a base station via at least the first antennagroup or the second antenna group.
 13. The user equipment of claim 12,wherein the first type precoding matrix is an antenna group selectionmatrix and the second type precoding matrix is a DFT matrix.
 14. Theuser equipment of claim 12, wherein the second type precoding matrixincludes a code in which the two components corresponding to the firstantenna group and the two components corresponding to the second antennagroup are mutually orthogonal.
 15. The user equipment of claim 12,wherein the 4-antenna codebook further includes a precoding matrix, inwhich two components corresponding to either the first antenna group orthe second antenna group are 0 in a first column and two componentscorresponding to either the second antenna group or the first antennagroup are 0 in a second column, for a rank of
 2. 16. The user equipmentof claim 15, wherein the 4-antenna codebook further includes at leastone selected from the group consisting of a precoding matrix forperforming a layer swapping function of changing positions of two layersignals and an antenna permutation precoding matrix for changing aposition of an antenna, for the rank of
 2. 17. The user equipment ofclaim 12, wherein each of the first type precoding matrix and the secondtype precoding matrix is a precoding matrix multiplied by a sameconstant.
 18. The user equipment of claim 17, wherein the first typeprecoding matrix is configured to transmit the precoded signal to thebase station using ½ of a maximum available transmission power of theuser equipment.
 19. A user equipment comprising: a first antenna groupincluding a first antenna and a second antenna; a second antenna groupincluding a third antenna and a fourth antenna; a memory configured tostore a 4-antenna codebook including a precoding matrix to turn off thefirst antenna group for a rank of 1; and a precoder outputting aprecoded signal by precoding a transmission signal using the precodingmatrix, wherein the precoded signal is transmitted to a base station viathe first antenna group, and wherein the precoding matrix includes twocomponents corresponding to the first antenna group that are zero andanother two components corresponding to the second antenna group thatconstruct a discrete Fourier transform (DFT) matrix.
 20. A base stationcomprising: an antenna configured to receive a reception signaltransmitted from a user equipment configured to transmit a signal using4 antennas grouped into a first antenna group including two of the 4antennas and a second antenna group including the other two of the 4antennas; a memory configured to store a 4-antenna codebook including afirst type precoding matrix, in which two components corresponding toone of the first and second antenna groups are zero and two componentscorresponding to the other one of the first and second antenna groupsconstruct a discrete Fourier transform (DFT) matrix, and a second typeprecoding matrix, in which two components corresponding to the firstantenna group and two components corresponding to the second antennagroup construct DFT matrixes for a rank of 1; and a precoder performingreverse processing of precoding on the reception signal by using aspecific precoding matrix corresponding to a transmission rank andprecoding matrix identification information used by the user equipment,wherein the specific precoding matrix is selected from the 4-antennacodebook.
 21. The base station of claim 20, wherein the 4-antennacodebook further includes a precoding matrix, in which two componentscorresponding to either the first antenna group or the second antennagroup are 0 in a first column and two components corresponding to eitherthe second antenna group or the first antenna group are 0 in a secondcolumn, for a rank of 2.